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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 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 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
 | Rohini Seth answered |
A composite number has more than two factors. 12 is composite because it has factors 1, 2, 3, 4, 6, and 12.
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 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 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
 | Muskaan Chavan answered |
Understanding Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simple terms, a prime number can only be divided evenly (without a remainder) by 1 and the number itself.
Analyzing the Given Options
Let’s evaluate each of the numbers provided:
Conclusion
Among the options given (21, 23, 25, 27), the only number that meets the definition of a prime number is 23. Thus, the correct answer is option 'B'. Understanding prime numbers is essential in mathematics as they serve as the building blocks for all other natural numbers.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simple terms, a prime number can only be divided evenly (without a remainder) by 1 and the number itself.
Analyzing the Given Options
Let’s evaluate each of the numbers provided:
- 21: This number can be divided by 1, 3, 7, and 21. Since it has divisors other than 1 and itself, it is not a prime number.
- 23: The only divisors of 23 are 1 and 23 itself. Therefore, it is a prime number.
- 25: This number can be divided by 1, 5, and 25. Having divisors other than 1 and itself confirms that it is not a prime number.
- 27: This number can be divided by 1, 3, 9, and 27. Since it has additional divisors, it is also not a prime number.
Conclusion
Among the options given (21, 23, 25, 27), the only number that meets the definition of a prime number is 23. Thus, the correct answer is option 'B'. Understanding prime numbers is essential in mathematics as they serve as the building blocks for all other natural numbers.
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 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
| | Anjali Sharma answered |
Understanding Co-prime Numbers
Co-prime numbers, also known as relatively prime numbers, are pairs of numbers that have no common factors other than 1. This means their greatest common divisor (GCD) is 1.
Analyzing the Options
Let’s evaluate each pair of numbers to determine if they are co-prime:
Option A: 4 and 9
- Factors of 4: 1, 2, 4
- Factors of 9: 1, 3, 9
- Common factors: 1
Since the only common factor is 1, 4 and 9 are co-prime.
Option B: 12 and 15
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 3
Since they share a common factor (3), they are not co-prime.
Option C: 18 and 24
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 6
Since they share multiple common factors, they are not co-prime.
Option D: 20 and 30
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 2, 5, 10
Again, since they share multiple common factors, they are not co-prime.
Conclusion
Hence, the only pair that qualifies as co-prime is Option A: 4 and 9. They have no common factors other than 1, making them relatively prime to each other.
Co-prime numbers, also known as relatively prime numbers, are pairs of numbers that have no common factors other than 1. This means their greatest common divisor (GCD) is 1.
Analyzing the Options
Let’s evaluate each pair of numbers to determine if they are co-prime:
Option A: 4 and 9
- Factors of 4: 1, 2, 4
- Factors of 9: 1, 3, 9
- Common factors: 1
Since the only common factor is 1, 4 and 9 are co-prime.
Option B: 12 and 15
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 3
Since they share a common factor (3), they are not co-prime.
Option C: 18 and 24
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 6
Since they share multiple common factors, they are not co-prime.
Option D: 20 and 30
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 2, 5, 10
Again, since they share multiple common factors, they are not co-prime.
Conclusion
Hence, the only pair that qualifies as co-prime is Option A: 4 and 9. They have no common factors other than 1, making them relatively prime to each other.
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.
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 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 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.
Which of the following numbers can be expressed as the product of exactly three different prime numbers?- a)20
- b)165
- c)45
- d)147
Correct answer is option 'B'. Can you explain this answer?
Which of the following numbers can be expressed as the product of exactly three different prime numbers?
a)
20
b)
165
c)
45
d)
147
 | Coders Trust answered |
(a) 20: Prime factorization: 20 = 2 × 2 × 5
It has only 2 distinct primes (2 and 5).
It has only 2 distinct primes (2 and 5).
(b) 165: Prime factorization: 165 = 3 × 5 × 11
It has exactly 3 distinct primes (3, 5, and 11).
It has exactly 3 distinct primes (3, 5, and 11).
(c) 45: Prime factorization: 45 = 3 × 3 × 5
It has only 2 distinct primes (3 and 5).
It has only 2 distinct primes (3 and 5).
(d) 147: Prime factorization: 147 = 3 × 7 × 7
It has only 2 distinct primes (3 and 7).
It has only 2 distinct primes (3 and 7).
The number that is the product of exactly three distinct prime numbers is: (b) 165
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.
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