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All questions of Prime Time for Class 6 Exam
What is the prime factorization of 60?- a)2 × 3 ×10
- b)2 × 5 × 6
- c)2 × 2 × 3 × 5
- d)3 × 5 × 4
Correct answer is option 'C'. Can you explain this answer?
What is the prime factorization of 60?
a)
2 × 3 ×10
b)
2 × 5 × 6
c)
2 × 2 × 3 × 5
d)
3 × 5 × 4
|
Shivam Chakraborty answered |
Understanding Prime Factorization
Prime factorization is the process of expressing a number as the product of its prime factors. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Finding the Prime Factorization of 60
To factorize 60, we can start by dividing it by the smallest prime number, which is 2.
- 60 ÷ 2 = 30 (2 is a prime factor)
- 30 ÷ 2 = 15 (2 is again a prime factor)
- 15 ÷ 3 = 5 (3 is a prime factor)
- 5 ÷ 5 = 1 (5 is a prime factor)
Now, we have expressed 60 as a product of prime factors:
Prime Factors of 60
- 2 (from the first division)
- 2 (from the second division)
- 3 (from the third division)
- 5 (from the fourth division)
Hence, the prime factorization of 60 is:
Final Expression
- 60 = 2 × 2 × 3 × 5
This can also be written as:
- 60 = 2² × 3 × 5
Conclusion
- Among the options given, option 'C' (2 × 2 × 3 × 5) correctly represents the prime factorization of 60.
- The other options do not consist solely of prime factors, making option 'C' the correct answer.
Prime factorization is the process of expressing a number as the product of its prime factors. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Finding the Prime Factorization of 60
To factorize 60, we can start by dividing it by the smallest prime number, which is 2.
- 60 ÷ 2 = 30 (2 is a prime factor)
- 30 ÷ 2 = 15 (2 is again a prime factor)
- 15 ÷ 3 = 5 (3 is a prime factor)
- 5 ÷ 5 = 1 (5 is a prime factor)
Now, we have expressed 60 as a product of prime factors:
Prime Factors of 60
- 2 (from the first division)
- 2 (from the second division)
- 3 (from the third division)
- 5 (from the fourth division)
Hence, the prime factorization of 60 is:
Final Expression
- 60 = 2 × 2 × 3 × 5
This can also be written as:
- 60 = 2² × 3 × 5
Conclusion
- Among the options given, option 'C' (2 × 2 × 3 × 5) correctly represents the prime factorization of 60.
- The other options do not consist solely of prime factors, making option 'C' the correct answer.
Which of these numbers is divisible by both 2 and 3?- a)4
- b)9
- c)12
- d)15
Correct answer is option 'C'. Can you explain this answer?
a)
4
b)
9
c)
12
d)
15
|
Aman Choudhury answered |
Divisibility by 2 and 3
To determine if a number is divisible by both 2 and 3, we need to look at the divisibility rules for each of these numbers.
Divisibility by 2:
A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. This is because these are all even numbers.
Divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, for the number 12, the sum of its digits is 1 + 2 = 3, which is divisible by 3.
Analysis of options:
a) 4 is not divisible by 3.
b) 9 is divisible by 3 but not by 2.
c) 12 is divisible by both 2 and 3 (1 + 2 = 3, and it ends in 2).
d) 15 is divisible by 3 but not by 2.
Therefore, the only number that is divisible by both 2 and 3 is option C) 12.
To determine if a number is divisible by both 2 and 3, we need to look at the divisibility rules for each of these numbers.
Divisibility by 2:
A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. This is because these are all even numbers.
Divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, for the number 12, the sum of its digits is 1 + 2 = 3, which is divisible by 3.
Analysis of options:
a) 4 is not divisible by 3.
b) 9 is divisible by 3 but not by 2.
c) 12 is divisible by both 2 and 3 (1 + 2 = 3, and it ends in 2).
d) 15 is divisible by 3 but not by 2.
Therefore, the only number that is divisible by both 2 and 3 is option C) 12.
How many prime numbers are there between 21 and 30?- a)1
- b)3
- c)2
- d)4
Correct answer is option 'C'. Can you explain this answer?
How many prime numbers are there between 21 and 30?
a)
1
b)
3
c)
2
d)
4
|
Kds Coaching answered |
The prime numbers between 21 and 30 are: 23, 29
Thus, there are a total of 2 prime numbers in this range.
Which of these numbers is composite?- a)5
- b)7
- c)11
- d)12
Correct answer is option 'D'. Can you explain this answer?
a)
5
b)
7
c)
11
d)
12
|
Bibek Verma answered |
Understanding Composite Numbers
Composite numbers are defined as numbers that have more than two distinct positive divisors. In other words, they can be divided evenly by numbers other than 1 and themselves.
Identifying Composite Numbers from the Options
Let’s analyze the given options:
Conclusion
Among the options provided, 12 stands out as the only composite number. The other numbers (5, 7, and 11) are all prime, with only two divisors each. Knowing how to categorize numbers as composite or prime is essential in mathematics, especially at this level of study.
Composite numbers are defined as numbers that have more than two distinct positive divisors. In other words, they can be divided evenly by numbers other than 1 and themselves.
Identifying Composite Numbers from the Options
Let’s analyze the given options:
- 5: This number has only two divisors, which are 1 and 5. Therefore, it is a prime number.
- 7: Similar to 5, 7 also has only two divisors: 1 and 7. Thus, it is a prime number.
- 11: This number, too, has just two divisors: 1 and 11. Hence, it is a prime number.
- 12: This number has several divisors: 1, 2, 3, 4, 6, and 12. Since it can be divided evenly by numbers other than 1 and itself, it is classified as a composite number.
Conclusion
Among the options provided, 12 stands out as the only composite number. The other numbers (5, 7, and 11) are all prime, with only two divisors each. Knowing how to categorize numbers as composite or prime is essential in mathematics, especially at this level of study.
Which number is a factor of both 14 and 36?- a)2
- b)3
- c)7
- d)12
Correct answer is option 'A'. Can you explain this answer?
a)
2
b)
3
c)
7
d)
12
|
Rahul Kumar answered |
2 is the only number that can divide both 14 and 36 evenly.
Which of the following numbers is a multiple of 4?- a)14
- b)18
- c)20
- d)22
Correct answer is option 'C'. Can you explain this answer?
a)
14
b)
18
c)
20
d)
22
|
Coachify answered |
A multiple of 4 is any number that can be divided evenly by 4. 20 ÷ 4 = 5, so 20 is a multiple of 4.
What is the prime factorization of 12?- a)2 × 2 × 3
- b)3 × 4
- c)2 × 6
- d)1 × 12
Correct answer is option 'A'. Can you explain this answer?
a)
2 × 2 × 3
b)
3 × 4
c)
2 × 6
d)
1 × 12
|
Eduskill Classes answered |
Prime factorization involves breaking a number down into prime factors. For 12, the prime factors are 2 × 2 × 3.
Which of the following numbers is not a multiple of 5?- a)10
- b)20
- c)30
- d)32
Correct answer is option 'D'. Can you explain this answer?
a)
10
b)
20
c)
30
d)
32
|
Gunjan Lakhani answered |
A multiple of 5 ends in 0 or 5. 32 does not end in 0 or 5, so it is not a multiple of 5.
Which of the following numbers is divisible by 8?- a)112
- b)118
- c)123
- d)130
Correct answer is option 'A'. Can you explain this answer?
Which of the following numbers is divisible by 8?
a)
112
b)
118
c)
123
d)
130
|
Kiran Das answered |
Understanding Divisibility by 8
To determine if a number is divisible by 8, we need to check if the last three digits of the number form a number that is divisible by 8. For numbers less than three digits, we consider the entire number.
Checking the Options
- Option A: 112
- Last three digits: 112
- Calculation: 112 ÷ 8 = 14
- Since 14 is a whole number, 112 is divisible by 8.
- Option B: 118
- Last three digits: 118
- Calculation: 118 ÷ 8 = 14.75
- Since 14.75 is not a whole number, 118 is not divisible by 8.
- Option C: 123
- Last three digits: 123
- Calculation: 123 ÷ 8 = 15.375
- Since 15.375 is not a whole number, 123 is not divisible by 8.
- Option D: 130
- Last three digits: 130
- Calculation: 130 ÷ 8 = 16.25
- Since 16.25 is not a whole number, 130 is not divisible by 8.
Conclusion
From the analysis above, the only number among the options provided that is divisible by 8 is 112. Therefore, the correct answer is option A.
To determine if a number is divisible by 8, we need to check if the last three digits of the number form a number that is divisible by 8. For numbers less than three digits, we consider the entire number.
Checking the Options
- Option A: 112
- Last three digits: 112
- Calculation: 112 ÷ 8 = 14
- Since 14 is a whole number, 112 is divisible by 8.
- Option B: 118
- Last three digits: 118
- Calculation: 118 ÷ 8 = 14.75
- Since 14.75 is not a whole number, 118 is not divisible by 8.
- Option C: 123
- Last three digits: 123
- Calculation: 123 ÷ 8 = 15.375
- Since 15.375 is not a whole number, 123 is not divisible by 8.
- Option D: 130
- Last three digits: 130
- Calculation: 130 ÷ 8 = 16.25
- Since 16.25 is not a whole number, 130 is not divisible by 8.
Conclusion
From the analysis above, the only number among the options provided that is divisible by 8 is 112. Therefore, the correct answer is option A.
What are the factors of 24?- a)1, 2, 3, 4, 6, 8, 12, 24
- b)1, 2, 4, 6, 12, 24
- c)1, 3, 8, 24
- d)1, 2, 3, 5, 24
Correct answer is option 'A'. Can you explain this answer?
What are the factors of 24?
a)
1, 2, 3, 4, 6, 8, 12, 24
b)
1, 2, 4, 6, 12, 24
c)
1, 3, 8, 24
d)
1, 2, 3, 5, 24
|
EduRev Class 6 answered |
A factor divides a number exactly. All these listed numbers divide 24 without any remainder.
Which of these is a prime number?- a)8
- b)9
- c)11
- d)12
Correct answer is option 'C'. Can you explain this answer?
a)
8
b)
9
c)
11
d)
12
|
Torcia Education answered |
A prime number has only two factors: 1 and itself. 11 is a prime number because it can only be divided by 1 and 11.
Which of these pairs of numbers are co-prime?- a)8 and 12
- b)14 and 21
- c)9 and 28
- d)15 and 20
Correct answer is option 'C'. Can you explain this answer?
a)
8 and 12
b)
14 and 21
c)
9 and 28
d)
15 and 20
|
Subset Academy answered |
Co-prime numbers have no common factors other than 1. 9 and 28 are co-prime because they have no common factors other than 1.
Which pair of numbers is co-prime?- a)4 and 9
- b)12 and 15
- c)18 and 24
- d)20 and 30
Correct answer is option 'A'. Can you explain this answer?
Which pair of numbers is co-prime?
a)
4 and 9
b)
12 and 15
c)
18 and 24
d)
20 and 30
|
|
Subset Academy answered |
Co-prime numbers have no common factor except 1. 4 and 9 share no common factors other than 1.
Which of these numbers is a factor of 24?- a)3
- b)5
- c)7
- d)9
Correct answer is option 'A'. Can you explain this answer?
a)
3
b)
5
c)
7
d)
9
|
Dr Manju Sen answered |
A factor of 24 is a number that divides 24 evenly. 3 is a factor of 24 because 24 ÷ 3 = 8.
What is the only common factor of 7 and 9?- a)7
- b)9
- c)1
- d)3
Correct answer is option 'C'. Can you explain this answer?
a)
7
b)
9
c)
1
d)
3
|
Rohini Seth answered |
The only common factor of 7 and 9 is 1 because 7 and 9 have no other factors in common.
What is the LCM (Least Common Multiple) of 3 and 5?- a)10
- b)12
- c)15
- d)30
Correct answer is option 'C'. Can you explain this answer?
a)
10
b)
12
c)
15
d)
30
|
|
Varun Jain answered |
Understanding LCM
The Least Common Multiple (LCM) of two numbers is the smallest multiple that is exactly divisible by both numbers. To find the LCM of 3 and 5, we can use a few different methods, such as listing multiples or using prime factorization.
Method 1: Listing Multiples
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Now, we find the smallest common multiple:
- The common multiples of 3 and 5 are 15, 30, ...
The smallest is 15.
Method 2: Prime Factorization
- Prime Factorization of 3: 3 (itself, as it's a prime number)
- Prime Factorization of 5: 5 (itself, also a prime number)
To find the LCM, we take the highest power of each prime factor:
- LCM = 3^1 * 5^1 = 15.
Conclusion
Based on both methods, the LCM of 3 and 5 is 15. Therefore, the correct answer is option 'C'.
Understanding how to find the LCM helps in solving problems related to fractions, ratios, and common denominators effectively.
The Least Common Multiple (LCM) of two numbers is the smallest multiple that is exactly divisible by both numbers. To find the LCM of 3 and 5, we can use a few different methods, such as listing multiples or using prime factorization.
Method 1: Listing Multiples
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Now, we find the smallest common multiple:
- The common multiples of 3 and 5 are 15, 30, ...
The smallest is 15.
Method 2: Prime Factorization
- Prime Factorization of 3: 3 (itself, as it's a prime number)
- Prime Factorization of 5: 5 (itself, also a prime number)
To find the LCM, we take the highest power of each prime factor:
- LCM = 3^1 * 5^1 = 15.
Conclusion
Based on both methods, the LCM of 3 and 5 is 15. Therefore, the correct answer is option 'C'.
Understanding how to find the LCM helps in solving problems related to fractions, ratios, and common denominators effectively.
What is the smallest prime number?- a)1
- b)2
- c)3
- d)5
Correct answer is option 'B'. Can you explain this answer?
a)
1
b)
2
c)
3
d)
5
|
|
EduRev Class 6 answered |
The smallest prime number is 2, as it can only be divided by 1 and 2.
Which of the following is a prime number?- a)21
- b)23
- c)25
- d)27
Correct answer is option 'B'. Can you explain this answer?
Which of the following is a prime number?
a)
21
b)
23
c)
25
d)
27
|
|
Subset Academy answered |
A prime number has only two factors: 1 and itself. 23 is only divisible by 1 and 23.
What is the prime factorization of 56?- a)2×2×2×7
- b)2×4×7
- c)8×7
- d)4×14
Correct answer is option 'A'. Can you explain this answer?
What is the prime factorization of 56?
a)
2×2×2×7
b)
2×4×7
c)
8×7
d)
4×14
|
|
Subset Academy answered |
The prime factorization includes only prime numbers, which here are 2 and 7.
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