# How to Solve Prime Factor Questions – Practice with Answer Key

- Posted by Brian Stocker MA
- Date April 7, 2014
- Comments 4 comments

## How to Prime Factors and Factorization

Factorization or *factoring* is writing a number or mathematical object as a product of several factors, generally smaller or simpler objects of the same kind.

### All about Prime Numbers

**What is a prime number?**

A prime number is a whole number greater than 1, only divisible by 1 and itself.

**What is the first prime number?**

The first prime number is 2.

**What is a composite number?**

A positive integer greater than 1 that is not a prime number.

**What is the difference between a prime number and a composite number?**

Both prime numbers and composite numbers are positive integers greater than 1. The difference a composite number is not a prime number.

### Prime Factors Practice Questions

**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

### Try a FREE Algebra Quiz

### Answer Key

**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.

## Tips for Solving Prime Number Questions

**1. Understand Prime Factors**

Prime factors are the prime numbers that multiply. For example, the prime factors of 28 are 2 and 7, 2 × 2 × 7 = 28

**2. Start with the Smallest Prime Number**

Start by dividing the number by the smallest prime, which is 2, and continue dividing by 2 until you can’t divide evenly.

**3. Move to the Next Prime Number**

Here, once 2 no longer divides evenly, try the next smallest prime number, 3.

**4. Repeat Repeat**

Repeat with subsequent primes (here, 5, 7, 11, 13, etc.) until the quotient is 1.

**5. Use a Prime Number Lists**

Use a list – see Wikipedia List of Primes

**6. Check Your Work**

Good advice for any question! Make sure the primes you found multiply to the answer.

**Tips for Efficiency**

**Memorize Small Primes ** The first few primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) will allow you to answer faster.

**Recognize Patterns:** For example, even numbers are always divisible by 2, and numbers ending in 0 or 5 are divisible by 5.

**Use Division Rules:** Know the rules for divisibility to quickly identify factors. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

**Factor Trees:** Draw a factor tree to break down the number into primes.

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Monday, April 7th, 2014

**Date Modified:**Friday, June 14th, 2024

## 4 Comments

this is a good website because it gives us extra practice for the test that’s coming up or soon.

Thank-you for posting this, it’s really helpful

it was a nice experience for me to correct my mistakes. Thanks for the one who prepared

Can you explain #5 better?