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All questions of Playing with Numbers for CTET & State TET Exam
If a number is divisible by 10, then which of the following can be its one’s digit?- a)0
- b)1
- c)3
- d)5
Correct answer is option 'A'. Can you explain this answer?
If a number is divisible by 10, then which of the following can be its one’s digit?
a)
0
b)
1
c)
3
d)
5
|
Priyanka Sharma answered |
A number is divisible by 10, if its ones digit is 0.
A number is divisible by 5, if its ones digit is 0 or 5.
A number is divisible by 5, if its ones digit is 0 or 5.
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Which of the following is the smallest prime number?
- a)2
- b)4
- c)3
- d)6
Correct answer is option 'A'. Can you explain this answer?
Which of the following is the smallest prime number?
a)
2
b)
4
c)
3
d)
6
|
Arjun Desai answered |
A prime number must have exactly two factors (1 and itself). Therefore, the number 2 is the lowest prime number as its only common divisors are 1 and 2. The number 1 only has 1 common divisor so it cannot be a prime number.
Tell the maximum number of consecutive numbers less than 100 so that there is no prime number between them.
- a)6
- b)5
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
Tell the maximum number of consecutive numbers less than 100 so that there is no prime number between them.
a)
6
b)
5
c)
7
d)
8
|
Abhishek Chakraborty answered |
For 7 consecutive composite numbers, there should be 2 prime numbers with atleast a difference of 8. And that's possible only between 89 and 97.
So the numbers are 90,91,92,93,94,95,96.
So the numbers are 90,91,92,93,94,95,96.
Which of the following number is divisible by 3?- a)121
- b)124
- c)123
- d)122
Correct answer is option 'C'. Can you explain this answer?
Which of the following number is divisible by 3?
a)
121
b)
124
c)
123
d)
122
|
Moumita Desai answered |
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
Two numbers having only 1 as common factor are called- a)Odd numbers
- b)prime numbers
- c)Co-prime numbers
- d)Composite numbers
Correct answer is option 'C'. Can you explain this answer?
Two numbers having only 1 as common factor are called
a)
Odd numbers
b)
prime numbers
c)
Co-prime numbers
d)
Composite numbers
|
Ananya Das answered |
The two numbers which have only 1 as their common factor are called co-primes.
If a number is divisible by 2 and 3 both then is divisible by- a)3
- b)6
- c)5
- d)7
Correct answer is option 'B'. Can you explain this answer?
If a number is divisible by 2 and 3 both then is divisible by
a)
3
b)
6
c)
5
d)
7
|
Surbhi Patel answered |
Divisibility Rules
- Divisibility rule of 2: If a number is even, it is divisible by 2.
- Divisibility rule of 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
- Divisibility rule of 6: If a number is divisible by both 2 and 3, then it is divisible by 6.
Explanation
- If a number is divisible by 2, it means it is an even number.
- If the sum of the digits of a number is divisible by 3, it means the number is divisible by 3.
- If a number is divisible by both 2 and 3, it means the number is even and the sum of its digits is also divisible by 3.
- Therefore, the number is also divisible by 6.
Conclusion
- Hence, if a number is divisible by 2 and 3 both, then it is divisible by 6.
- Therefore, the correct answer is option 'B'.
- Divisibility rule of 2: If a number is even, it is divisible by 2.
- Divisibility rule of 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
- Divisibility rule of 6: If a number is divisible by both 2 and 3, then it is divisible by 6.
Explanation
- If a number is divisible by 2, it means it is an even number.
- If the sum of the digits of a number is divisible by 3, it means the number is divisible by 3.
- If a number is divisible by both 2 and 3, it means the number is even and the sum of its digits is also divisible by 3.
- Therefore, the number is also divisible by 6.
Conclusion
- Hence, if a number is divisible by 2 and 3 both, then it is divisible by 6.
- Therefore, the correct answer is option 'B'.
The smallest composite number is- a)2
- b)1
- c)4
- d)3
Correct answer is option 'C'. Can you explain this answer?
The smallest composite number is
a)
2
b)
1
c)
4
d)
3
|
Upasana Basak answered |
The smallest composite number is 4
So option C is the correct answer.
The successor of every even number is- a)even
- b)prime
- c)odd
- d)composite.
Correct answer is option 'C'. Can you explain this answer?
The successor of every even number is
a)
even
b)
prime
c)
odd
d)
composite.
|
Varun Kapoor answered |
Even numbers are 2,4,6,8,10 and so on.
In between these even numbers, we have odd numbers 3,5,7,9..
Hence, successor of even number, is an odd number.
Can you explain the answer of this question below:The only prime number which is also even is
- A:
6
- B:
1
- C:
2
- D:
4
The answer is C.
The only prime number which is also even is
6
1
2
4
|
Raksha Roy answered |
2 is the only even Prime Number. More interesting fact is that 2 is the smallest prime number. Many of us has the misconception that 1 is the smallest prime number, but as per standard definition of prime number “A number which has 2 factors 1 and itself is said to be a prime number.”
Find the HCF of 27, 63.- a)2
- b)6
- c)3
- d)9
Correct answer is option 'D'. Can you explain this answer?
Find the HCF of 27, 63.
a)
2
b)
6
c)
3
d)
9
|
Arshiya Sen answered |
Factors of 27 = 3 x 3 x 3
Factors of 63 = 3 x 3 x 7
H.C.F. (27, 63) = 3 x 3 = 9
A number is divisible by 4 if its- a)last digit is 0
- b)last digit is 4
- c)last two digits are divisible by 4
- d)last digit is 8
Correct answer is option 'C'. Can you explain this answer?
A number is divisible by 4 if its
a)
last digit is 0
b)
last digit is 4
c)
last two digits are divisible by 4
d)
last digit is 8
|
|
Amit Sharma answered |
Whole numbers are divisible by 4 if the number formed by the last two individual digits is evenly divisible by 4.
For example, the number formed by the last two digits of the number 3628 is 28, which is evenly divisible by 4 so the number 3628 is evenly divisible by 4.
Every prime number except ______ is odd.- a)5
- b)7
- c)2
- d)3
Correct answer is option 'C'. Can you explain this answer?
Every prime number except ______ is odd.
a)
5
b)
7
c)
2
d)
3
|
Aryan Desai answered |
Every prime number is divisible only by itself. 1 and 2 is the smallest even number that is followed by condition that is so it as even prime number.
These numbers have been taken and divisible by 2 so expect 2 all prime numbers are odd. There is no exception and number 2 is prime even number.
A number is divisible by 12. By what other numbers will that number be divisible?
- a)3 and 5
- b)4 and 7
- c)3 and 7
- d)3 and 4
Correct answer is option 'D'. Can you explain this answer?
A number is divisible by 12. By what other numbers will that number be divisible?
a)
3 and 5
b)
4 and 7
c)
3 and 7
d)
3 and 4
|
|
Maya Mehta answered |
To determine the numbers by which a given number will be divisible, we need to consider the factors of that number. In this case, we are given that the number is divisible by 12.
Factors of 12:
The factors of 12 are the numbers that divide 12 without leaving a remainder. These factors are 1, 2, 3, 4, 6, and 12.
Divisibility by 3:
To determine if a number is divisible by 3, we need to check if the sum of its digits is divisible by 3. In the case of 12, the sum of its digits (1 + 2) is 3, which is divisible by 3. Therefore, 12 is divisible by 3.
Divisibility by 4:
To determine if a number is divisible by 4, we need to check if the last two digits form a number that is divisible by 4. In the case of 12, the last two digits are 12 itself, which is divisible by 4. Therefore, 12 is divisible by 4.
So, the numbers by which 12 will be divisible are 1, 2, 3, 4, 6, and 12.
Out of the given options, the correct answer is option 'D' (3 and 4) because both 3 and 4 are factors of 12.
Factors of 12:
The factors of 12 are the numbers that divide 12 without leaving a remainder. These factors are 1, 2, 3, 4, 6, and 12.
Divisibility by 3:
To determine if a number is divisible by 3, we need to check if the sum of its digits is divisible by 3. In the case of 12, the sum of its digits (1 + 2) is 3, which is divisible by 3. Therefore, 12 is divisible by 3.
Divisibility by 4:
To determine if a number is divisible by 4, we need to check if the last two digits form a number that is divisible by 4. In the case of 12, the last two digits are 12 itself, which is divisible by 4. Therefore, 12 is divisible by 4.
So, the numbers by which 12 will be divisible are 1, 2, 3, 4, 6, and 12.
Out of the given options, the correct answer is option 'D' (3 and 4) because both 3 and 4 are factors of 12.
_____ is the factor of 68.- a)6
- b)5
- c)3
- d)17
Correct answer is option 'D'. Can you explain this answer?
_____ is the factor of 68.
a)
6
b)
5
c)
3
d)
17
|
Shreya Iyer answered |
Factors of 68 are 1, 2, 4, 17, 34, 68
What are the numbers which have more than two factors called?- a)Even numbers
- b)Prime numbers
- c)Composite numbers
- d)Odd numbers
Correct answer is option 'C'. Can you explain this answer?
What are the numbers which have more than two factors called?
a)
Even numbers
b)
Prime numbers
c)
Composite numbers
d)
Odd numbers
|
Siddharth Nambiar answered |
Numbers which have more than two factors are called composite numbers.
What is the H.C.F. of two co-prime numbers?- a)1
- b)0
- c)2
- d)4
Correct answer is option 'A'. Can you explain this answer?
What is the H.C.F. of two co-prime numbers?
a)
1
b)
0
c)
2
d)
4
|
Jhanvi Banerjee answered |
H.C.F. of two co-prime numbers is 1.
If a number is divisible by 10, then which of the following can be its one’s digit?
- a)2
- b)3
- c)4
- d)0
Correct answer is option 'D'. Can you explain this answer?
If a number is divisible by 10, then which of the following can be its one’s digit?
a)
2
b)
3
c)
4
d)
0
|
Keerthana Menon answered |
If a number is divisible by 10, then its one's digit can only be 0. This is because any number divisible by 10 must end in 0.
If a number is divisible by each of two co-prime numbers than it is divisible by their
- a)difference also
- b)sum also
- c)quotient also
- d)product also
Correct answer is option 'D'. Can you explain this answer?
If a number is divisible by each of two co-prime numbers than it is divisible by their
a)
difference also
b)
sum also
c)
quotient also
d)
product also
|
Rajeev Sen answered |
If a number is divisible by each of two or more co-prime numbers then it is divisible by their products.
Every ______ of a number is greater than or equal to that number.- a)factor
- b)number
- c)multiple
- d)none to these
Correct answer is option 'C'. Can you explain this answer?
Every ______ of a number is greater than or equal to that number.
a)
factor
b)
number
c)
multiple
d)
none to these
|
Aman Choudhury answered |
The correct answer is option 'C': multiple.
Explanation:
To understand why the correct answer is 'multiple', let's first define what a multiple is. A multiple of a number is the result of multiplying that number by an integer (whole number). For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
Now, let's consider the given statement: "Every ______ of a number is greater than or equal to that number." This statement implies that whatever fills the blank, it should be something that, when multiplied by a number, the result is greater than or equal to the original number.
Let's consider the options provided:
a) Factor: A factor of a number is a whole number that divides the given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. However, if we multiply a number by one of its factors, the result may or may not be greater than the original number. For instance, if we multiply 12 by 2, we get 24, which is greater than 12, but if we multiply 12 by 3, we get 36, which is greater than 12. Therefore, a factor is not always greater than or equal to the original number.
b) Number: This option is incorrect because it is too broad. The statement is already referring to a number, so it doesn't provide any additional information.
c) Multiple: A multiple of a number, as mentioned earlier, is obtained by multiplying the number by an integer. Since we are multiplying the number, the resulting multiple will always be greater than or equal to the original number. For example, if we multiply 5 by 2, we get 10, which is greater than 5. Similarly, if we multiply 5 by 1, we get 5, which is equal to the original number. Therefore, every multiple of a number is greater than or equal to that number.
d) None of these: This option is incorrect because the correct answer is 'C' - multiple.
In conclusion, the correct answer is 'C' - multiple because every multiple of a number is greater than or equal to that number.
Explanation:
To understand why the correct answer is 'multiple', let's first define what a multiple is. A multiple of a number is the result of multiplying that number by an integer (whole number). For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
Now, let's consider the given statement: "Every ______ of a number is greater than or equal to that number." This statement implies that whatever fills the blank, it should be something that, when multiplied by a number, the result is greater than or equal to the original number.
Let's consider the options provided:
a) Factor: A factor of a number is a whole number that divides the given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. However, if we multiply a number by one of its factors, the result may or may not be greater than the original number. For instance, if we multiply 12 by 2, we get 24, which is greater than 12, but if we multiply 12 by 3, we get 36, which is greater than 12. Therefore, a factor is not always greater than or equal to the original number.
b) Number: This option is incorrect because it is too broad. The statement is already referring to a number, so it doesn't provide any additional information.
c) Multiple: A multiple of a number, as mentioned earlier, is obtained by multiplying the number by an integer. Since we are multiplying the number, the resulting multiple will always be greater than or equal to the original number. For example, if we multiply 5 by 2, we get 10, which is greater than 5. Similarly, if we multiply 5 by 1, we get 5, which is equal to the original number. Therefore, every multiple of a number is greater than or equal to that number.
d) None of these: This option is incorrect because the correct answer is 'C' - multiple.
In conclusion, the correct answer is 'C' - multiple because every multiple of a number is greater than or equal to that number.
What is the number of prime numbers between 50 and 60?- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
What is the number of prime numbers between 50 and 60?
a)
1
b)
2
c)
3
d)
4
|
|
Amit Sharma answered |
53 and 59 are the prime number between 50 and 60
901153 is divisible by ___.- a)3
- b)5
- c)11
- d)7
Correct answer is option 'C'. Can you explain this answer?
901153 is divisible by ___.
a)
3
b)
5
c)
11
d)
7
|
Harshitha Mukherjee answered |
901153
Sum of odd digits = 9 + 1 + 5 = 15
Sum of even digits = 0 + 1 + 3 = 4
Difference = 15-4 = 11
Difference is divisible by 11. Therefore, 901153 is divisible by 11.
The sum of two odd and one even numbers is
- a)Even
- b)Prime
- c)odd Composite
- d)Odd
Correct answer is option 'A'. Can you explain this answer?
The sum of two odd and one even numbers is
a)
Even
b)
Prime
c)
odd Composite
d)
Odd
|
Rajat Chatterjee answered |
We know that sum of two odd numbers is always even. Adding one more even number will keep the result an even number.
What is the L.C.M. of 17 and 5?- a)105
- b)95
- c)85
- d)5
Correct answer is option 'C'. Can you explain this answer?
What is the L.C.M. of 17 and 5?
a)
105
b)
95
c)
85
d)
5
|
Anand Patel answered |
Solution:
To find the LCM of 17 and 5, we need to follow the below steps:
Step 1: Prime factorization of 17 and 5.
- 17 is a prime number, so its prime factorization is 17.
- 5 is also a prime number, so its prime factorization is 5.
Step 2: Write the factors of both numbers.
- Factors of 17: 1, 17
- Factors of 5: 1, 5
Step 3: Find the common factors of both numbers.
- Common factors of 17 and 5: 1
Step 4: Multiply the common factors.
- 1 x 17 x 5 = 85
Therefore, the LCM of 17 and 5 is 85.
Hence, option C is the correct answer.
To find the LCM of 17 and 5, we need to follow the below steps:
Step 1: Prime factorization of 17 and 5.
- 17 is a prime number, so its prime factorization is 17.
- 5 is also a prime number, so its prime factorization is 5.
Step 2: Write the factors of both numbers.
- Factors of 17: 1, 17
- Factors of 5: 1, 5
Step 3: Find the common factors of both numbers.
- Common factors of 17 and 5: 1
Step 4: Multiply the common factors.
- 1 x 17 x 5 = 85
Therefore, the LCM of 17 and 5 is 85.
Hence, option C is the correct answer.
A is the 5th prime number. B is the 7th prime number. What is B - A?- a)6
- b)8
- c)12
- d)2
Correct answer is option 'A'. Can you explain this answer?
A is the 5th prime number. B is the 7th prime number. What is B - A?
a)
6
b)
8
c)
12
d)
2
|
Ishan Choudhury answered |
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
A = 11 and
B = 17
17-11 = 6
B = 17
17-11 = 6
The HCF of two consecutive numbers is- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
The HCF of two consecutive numbers is
a)
0
b)
1
c)
2
d)
3
|
|
Arjun Desai answered |
HCF of two consecutive numbers is always 1 . explanation : Take two consecutive numbers as 9 and 10. between these two numbers there is no common factor other than 1. Take two consecutive numbers as 17 and 18.
Which of them is prime number?- a)3
- b)6
- c)9
- d)8
Correct answer is option 'A'. Can you explain this answer?
Which of them is prime number?
a)
3
b)
6
c)
9
d)
8
|
|
Shreya Iyer answered |
3 is a prime number because it has only two distinct divisors: 1 and itself (3).
As a consequence, 3 is only a multiple of 1 and 3..
Since 3 is a prime number, 3 is also a deficient number, that is to say 3 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 3 without 3 itself (that is 1, by definition!).
Which of the following is the prime factorisation of 140?- a)2 × 2 × 7
- b)2 × 2 × 5
- c)2 × 2 × 5 × 7
- d)2 × 2 × 5 × 7 × 3
Correct answer is option 'C'. Can you explain this answer?
Which of the following is the prime factorisation of 140?
a)
2 × 2 × 7
b)
2 × 2 × 5
c)
2 × 2 × 5 × 7
d)
2 × 2 × 5 × 7 × 3
|
|
Ananya Das answered |
A: 2 × 2 × 7 = 28
B: 2 × 2 × 5 = 20
C: 2 × 2 × 5 × 7 = 140
D: 2 × 2 × 5 × 7 × 3 = 420
Which of the following is an example of an even number?- a)10351
- b)20989
- c)69007
- d)973572
Correct answer is option 'D'. Can you explain this answer?
Which of the following is an example of an even number?
a)
10351
b)
20989
c)
69007
d)
973572
|
|
Siddharth Nambiar answered |
Of the given options 973572 is an even number.
A number is divisible by 6. By what other numbers will that number be divisible
- a)3 and 4
- b)2 and 5
- c)2 and 3
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
A number is divisible by 6. By what other numbers will that number be divisible
a)
3 and 4
b)
2 and 5
c)
2 and 3
d)
None of these
|
|
Harshad Goyal answered |
Solution:
To understand the solution, we need to know the divisibility rules of 6.
Divisibility Rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Now, let us consider each option one by one.
a) 3 and 4: If a number is divisible by 3 and 4, it doesn't mean that it is divisible by 6. For example, the number 12 is divisible by 3 and 4, but it is also divisible by 6. However, the number 8 is divisible by 4 but not by 6. Hence, option a) is incorrect.
b) 2 and 5: If a number is divisible by 2 and 5, it doesn't mean that it is divisible by 6. For example, the number 10 is divisible by 2 and 5, but it is not divisible by 6. Hence, option b) is incorrect.
c) 2 and 3: According to the divisibility rule of 6, if a number is divisible by 2 and 3, it is also divisible by 6. Hence, option c) is correct.
d) None of these: Since option c) is correct, option d) is incorrect.
Therefore, the correct option is c) 2 and 3.
To understand the solution, we need to know the divisibility rules of 6.
Divisibility Rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Now, let us consider each option one by one.
a) 3 and 4: If a number is divisible by 3 and 4, it doesn't mean that it is divisible by 6. For example, the number 12 is divisible by 3 and 4, but it is also divisible by 6. However, the number 8 is divisible by 4 but not by 6. Hence, option a) is incorrect.
b) 2 and 5: If a number is divisible by 2 and 5, it doesn't mean that it is divisible by 6. For example, the number 10 is divisible by 2 and 5, but it is not divisible by 6. Hence, option b) is incorrect.
c) 2 and 3: According to the divisibility rule of 6, if a number is divisible by 2 and 3, it is also divisible by 6. Hence, option c) is correct.
d) None of these: Since option c) is correct, option d) is incorrect.
Therefore, the correct option is c) 2 and 3.
What is the H.C.F. of the two numbers equal to?- a)Product of the numbers ÷ their L.C.M.
- b)Product of the numbers × their L.C.M.
- c)Product of the numbers.
- d)Quotient of the numbers.
Correct answer is option 'A'. Can you explain this answer?
What is the H.C.F. of the two numbers equal to?
a)
Product of the numbers ÷ their L.C.M.
b)
Product of the numbers × their L.C.M.
c)
Product of the numbers.
d)
Quotient of the numbers.
|
|
Sagar Gupta answered |
Cannot be determined from the given information. The H.C.F. depends on the actual values of the two numbers.
What do you get when you multiply two factors?- a)Sum
- b)Product
- c)Difference
- d)Quotient
Correct answer is option 'B'. Can you explain this answer?
What do you get when you multiply two factors?
a)
Sum
b)
Product
c)
Difference
d)
Quotient
|
Pragati Khanna answered |
When two factors are multiplied we get a product.
Tell the maximum consecutive numbers less than 100 so that there is no prime number between them.- a)6
- b)5
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
Tell the maximum consecutive numbers less than 100 so that there is no prime number between them.
a)
6
b)
5
c)
7
d)
8
|
Nandita Choudhary answered |
For 7 consecutive composite numbers, there should be 2 prime numbers with atleast a difference of 8. And that's possible only between 89 and 97.
So the numbers are 90,91,92,93,94,95,96.
So the numbers are 90,91,92,93,94,95,96.
Which of them is composite number?- a)6
- b)5
- c)7
- d)3
Correct answer is option 'A'. Can you explain this answer?
Which of them is composite number?
a)
6
b)
5
c)
7
d)
3
|
|
Anita Menon answered |
A natural number greater than 1 that is not prime is called a composite number.
The only prime number which is also even is- a)6
- b)1
- c)2
- d)4
Correct answer is option 'C'. Can you explain this answer?
The only prime number which is also even is
a)
6
b)
1
c)
2
d)
4
|
Anjana Rane answered |
A prime number can have only 1 and itself as factors.
Any even number has 2 as a factor so if the number has itself , 2 and 1 as factors it can not be prime.
2 is an even number that has only itself and 1 as factors so it is the only even number that is a prime.
What are the numbers which are multiples of 2 called?- a)Odd numbers
- b)Even numbers
- c)Prime numbers
- d)Composite numbers
Correct answer is option 'B'. Can you explain this answer?
What are the numbers which are multiples of 2 called?
a)
Odd numbers
b)
Even numbers
c)
Prime numbers
d)
Composite numbers
|
|
Shooky Shadow 💜 answered |
All multiples of 2 number are called Even numbers.
Which of the following is the L.C.M. of 36 and 72?- a)36
- b)72
- c)108
- d)2
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the L.C.M. of 36 and 72?
a)
36
b)
72
c)
108
d)
2
|
|
Ishan Choudhury answered |
The prime factorization of 36 is: 2 x 2 x 3 x 3
The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get LCM = 2 x 2 x 2 x 3 x 3 = 72
The exact divisor of number 9 is- a)3
- b)2
- c)5
- d)4
Correct answer is option 'A'. Can you explain this answer?
The exact divisor of number 9 is
a)
3
b)
2
c)
5
d)
4
|
Kunal Mehta answered |
We know 3 x 3 = 9. So The exact divisor of number 9.
Number of factors of a given number are _______.- a)finite
- b)infinite
- c)3
- d)2
Correct answer is option 'A'. Can you explain this answer?
Number of factors of a given number are _______.
a)
finite
b)
infinite
c)
3
d)
2
|
Geetika Shah answered |
Factors of a number are defined as numbers or algebraic expressions that divide a given number/expression evenly. We can also say, factors are the numbers which are multiplied to get the other number. For example, 1, 3 and 9 are the factors of 9, because 1 × 9 = 9 and 3 × 3 = 9.
So the number of factors of a given number are finite.
Give an example for twin primes.- a)5, 11
- b)3, 5
- c)11, 17
- d)3, 7
Correct answer is option 'B'. Can you explain this answer?
Give an example for twin primes.
a)
5, 11
b)
3, 5
c)
11, 17
d)
3, 7
|
Rishika Chopra answered |
The first few twin prime pairs are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), … ... Five is the only prime in two distinct pairs.
What is the H.C.F. of 17 and 5?- a)1
- b)5
- c)17
- d)85
Correct answer is option 'A'. Can you explain this answer?
What is the H.C.F. of 17 and 5?
a)
1
b)
5
c)
17
d)
85
|
|
Geetika Shah answered |
No factor except 1 is common to them.
What are the numbers which have only two factors (1 and the number itself) called?- a)Composite numbers
- b)Even numbers
- c)Prime numbers
- d)Odd numbers
Correct answer is option 'C'. Can you explain this answer?
What are the numbers which have only two factors (1 and the number itself) called?
a)
Composite numbers
b)
Even numbers
c)
Prime numbers
d)
Odd numbers
|
Anoushka Banerjee answered |
Numbers which have only two factors (1 and itself) are called prime numbers.
The number of multiples of a given number is _______.- a)2
- b)finite
- c)infinite
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The number of multiples of a given number is _______.
a)
2
b)
finite
c)
infinite
d)
None of these
|
|
Ananya Das answered |
The number of multiples of a given number is infinite. Example : Multiples of 2 = {2,4,6,8,10,...} Multiples of 3 = { 3,6,9,12,15,18,...}
Find the HCF of 18, 48.- a)7
- b)6
- c)5
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Find the HCF of 18, 48.
a)
7
b)
6
c)
5
d)
None of these
|
|
Abhishek Chakraborty answered |
So, Factors of 18 = 2 x 3 x 3
Factors of 48 = 2 x 2 x 2 x 2 x 3
H.C.F. (18, 48) = 2 x 3 = 6
If a number is divisible by 5, then which of the following can be its one’s digit?
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'D'. Can you explain this answer?
If a number is divisible by 5, then which of the following can be its one’s digit?
a)
2
b)
3
c)
4
d)
5
|
|
Ishan Choudhury answered |
A number is divisible by 5 if the one's digit of the number is 0 or 5.
Which of these numbers is a factor of every number?- a)0
- b)1
- c)2
- d)4
Correct answer is option 'B'. Can you explain this answer?
Which of these numbers is a factor of every number?
a)
0
b)
1
c)
2
d)
4
|
|
Anita Menon answered |
1 is a factor of every number.
Which is the number that is neither prime nor composite?
- a)6
- b)1
- c)2
- d)5
Correct answer is option 'B'. Can you explain this answer?
Which is the number that is neither prime nor composite?
a)
6
b)
1
c)
2
d)
5
|
Dishani Pillai answered |
Explanation:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
A composite number is a positive integer that has at least one positive divisor other than one or itself.
The number 1 is neither prime nor composite.
Reasoning:
A prime number has exactly two factors, 1 and itself. For instance, 2 is a prime number since the only factors of 2 are 1 and 2.
A composite number has more than two factors. For instance, 6 is a composite number since it has four factors: 1, 2, 3, and 6.
The number 1 has only one factor, namely 1. Therefore, it is neither prime nor composite.
Answer:
The number that is neither prime nor composite is 1.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
A composite number is a positive integer that has at least one positive divisor other than one or itself.
The number 1 is neither prime nor composite.
Reasoning:
A prime number has exactly two factors, 1 and itself. For instance, 2 is a prime number since the only factors of 2 are 1 and 2.
A composite number has more than two factors. For instance, 6 is a composite number since it has four factors: 1, 2, 3, and 6.
The number 1 has only one factor, namely 1. Therefore, it is neither prime nor composite.
Answer:
The number that is neither prime nor composite is 1.
How many prime numbers are there between 1 and 50?- a)18
- b)12
- c)15
- d)20
Correct answer is option 'C'. Can you explain this answer?
How many prime numbers are there between 1 and 50?
a)
18
b)
12
c)
15
d)
20
|
Prasad Chawla answered |
Ans.
There is 15 prime no between 1 to 50 always remember 1 is not a prime no because according to prime no definition if given no is divisible by self and 1 that's know as prime no in other words you can say no is divisible by two no’s self and one and now if you go through definition of prime no ,“1” is not satisfied it also you can say “1” is divisible by only one no that's it self so that is why “1”is not a prime no ,so these are all possible prime no between 1 to 50
“2,3,5,7,11,13,17,19,23,29,31,37,41,43,47”
What is the H.C.F. of 120, 144 and 216?- a)38
- b)24
- c)120
- d)144
Correct answer is option 'B'. Can you explain this answer?
What is the H.C.F. of 120, 144 and 216?
a)
38
b)
24
c)
120
d)
144
|
|
Anoushka Banerjee answered |
∴ H.C.F. of 120 & 144 =24
Every number is a _____ and a _____ of itself.- a)factor, multiple
- b)prime, composite
- c)even, odd
- d)prime, twin prime
Correct answer is option 'A'. Can you explain this answer?
Every number is a _____ and a _____ of itself.
a)
factor, multiple
b)
prime, composite
c)
even, odd
d)
prime, twin prime
|
Atharv Naik answered |
Eg: 12 Factors: 1,2,3,4,6,12
12 Multiples: 12, 24, 36,48,so on
The same is for every number.
Therfore, every number is the factor and multiple of itself.
12 Multiples: 12, 24, 36,48,so on
The same is for every number.
Therfore, every number is the factor and multiple of itself.
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Mathematics & Pedagogy Paper 2 for CTET & TET Exams
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