How to Prime Factors – Practice with Answer Key

1. What are the prime factors of 17?

a. 2 x 8.5
b. 17
c. 3 x 5.5
d. None of the above

2. What are the prime factors of 100?

a. 2 x 2 x 5 x 5
b. 4 x 25
c. 2 x 2 x 2 x 5 x 5
d. 2 x 50

3. What are the prime factors of 25?

a. 4 x 5.5
b. 5 x 5 x 5
c. 1 x 25
d. 5 x 5

4. What are the prime factors of 81?

a. 3 x 3 x 9
b. 3 x 27
c. 3 x 3 x 3 x 3
d. All of the above

5. What are the prime factors of 125?

a. 5 x 25
b. 5 x 5 x 5
c. All of the above
d. None of the above

6. What are the prime factors of 132?

a. 4 x 3 x 11
b. 2 x 2 x 2 x 3 x 11
c. 2 x 6 x 11
d. 2 x 2 x 3 x 11

1. B
The only prime number that can divide 17 is 17.

2. A
To make it easier we can break this large number to two smaller numbers, 2 x 50 or 4 x 25. Let’s use 4 x 25. The prime factors of 4 = 2 x 2, and the prime factors of 25 = 5 x 5. The prime factors of 100 = 2 x 2 x 5 x 5.

3. D
The smallest prime number that can divide 25 is 5. 25/5 = 5. Prime factors of 25 = 5 x 5.

4. C
To make this easier we can break 81 to be 9 x 9 and then find the prime factors of each of these prime numbers. The prime factors of 9 = 3 x 3 and the prime factors of 9 = 3 x 3 Prime factors of 81 = 3 x 3 x 3 x 3.

5.  B
The smallest prime number that can divide 125 is 5. 125/5 = 25. 25/5 =5. Prime factors of 125 = 5 x 5 x5

6. D
The smallest prime number to divide 132 is 2. 132/2 = 66. 66/2 = 33. 33/3 = 11. 11 cannot be divided further by a prime number other than 11. The prime numbers of 132 = 2 x 2 x 3 x 11.