Solved Questions of Factors and Multiples
1. What is the prime factorization of 84?
a) 2 × 2 × 3 × 7
b) 2 × 2 × 3 × 11
c) 3 × 3 × 7 × 7
d) 2 × 2 × 2 × 11
Answer: a) 2 × 2 × 3 × 7
Explanation: To find the prime factorization of 84, we can start by dividing 84 by the smallest prime number, which is 2, to get 42. Then we can divide 42 by 2 again to get 21. We can continue this process until we get to 3 × 7, which are both prime numbers.
So, the prime factorization of 84 is 2 × 2 × 3 × 7.
2. What is the greatest common factor of 36 and 48?
a) 12
b) 18
c) 24
d) 36
Answer: a) 12
Explanation: To find the greatest common factor (GCF) of 36 and 48, we can list the factors of each number and find the largest factor that they have in common. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The largest factor that they have in common is 12, so the GCF of 36 and 48 is 12.
3. Which of the following is a multiple of both 6 and 8?
a) 12
b) 24
c) 36
d) 42
Answer: b) 24
Explanation: To find a multiple of both 6 and 8, we can list the multiples of each number and look for a number that appears in both lists. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, and so on.
The only number that appears in both lists is 24, so 24 is a multiple of both 6 and 8.
4. What is the least common multiple of 15 and 21?
a) 35
b) 105
c) 315
d) 525
Answer: b) 105
Explanation: To find the least common multiple (LCM) of 15 and 21, we can list the multiples of each number until we find the smallest multiple that they have in common. The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, and so on. The multiples of 21 are 21, 42, 63, 84, 105, and so on.
The smallest multiple that they have in common is 105, so the LCM of 15 and 21 is 105.
5. What is the sum of all the factors of 24?
a) 36
b) 48
c) 60
d) 72
Answer: d) 60
Explanation: To find the sum of all the factors of 24, we can list the factors of 24 and add them up. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Practice Questions of Factors and Multiples
1. What is the greatest common factor between 12 and 18?
a) 3
b) 6
c) 9
d) 12
Answer: b) 6
2. Which of the following is a multiple of 8?
a) 12
b) 15
c) 16
d) 20
Answer: c) 16
3. Which of the following is not a factor of 24?
a) 1
b) 2
c) 5
d) 8
Answer: c) 5
4. What is the least common multiple of 6 and 8?
a) 12
b) 24
c) 48
d) 96
Answer: b) 24
5. What is the prime factorization of 60?
a) 2 x 2 x 15
b) 2 x 3 x 10
c) 2 x 2 x 3 x 5
d) 2 x 2 x 2 x 3 x 5
Answer: c) 2 x 2 x 3 x 5
6. What is the smallest positive integer that is divisible by all the numbers from 1 to 10?
a) 2520
b) 5040
c) 720
d) 120
Answer: a) 2520
7. What is the next multiple of 7 after 49,021?
a) 49,028
b) 49,056
c) 49,062
d) 49,064
Answer: a) 49,028
8. What is the largest two-digit prime number that is a factor of 123?
a) 53
b) 49
c) 43
d) 41
Answer: d) 41
9. What is the prime factors of 140?
a) 5 x 5 x 8
b) 2 x 2 x 5 x 7
c) 2 x 2 x 5
d) 2 x 3 x 6
Answer: b) 2 x 2 x 5 x 7
10. What is the greatest common factor of 105 and 140?
a) 5
b) 7
c) 35
d) 55
Answer: c) 35
