## What are prime factors?

We know that factors are the numbers that divide perfectly into another number without a remainder. So, prime factors are all the prime numbers that divide perfectly into our number without a remainder.

*Example: Find the prime factors of 130*

## Steps:

- Let’s start by thinking about the first 5 prime numbers. These are 2, 3, 5, 7, and 11.
- Now we try to divide our number by the first prime number., e.g. 130 ÷ 2 = 65. We write down 2 as a prime factor.
- If our number is divisible by the prime number, then we repeat step 2, with the answer we got, e.g. 65 ÷ 2 = 32,5, so 2 is not another prime factor, and we try 3. e.g. 65 ÷ 3 = 21.6666… So 3 is not a prime factor and we try 5. 65 ÷ 5 = 13. We write down 5 as the next prime factor.
- We can see that 13 is a prime number, so we have found all our prime factors ⇒ 130 = 2 x 5 x 13.

*Let’s do another example: Find the prime factors of 64. *

- 64 ÷ 2 = 32
- then 32 ÷ 2 = 16
- then 16 ÷ 2 = 8
- and 8 ÷ 2 = 4
- and 4 ÷ 2 = 2
- and finally 2 ÷ 2 = 1
- So our prime factors are ⇒ 64 = 2 x 2 x 2 x 2 x 2 x 2 or 2
^{6}

*Let’s do one more example: Find the prime factors of 300. *

- 300 ÷ 2 = 150
- 150 ÷ 2 = 75 (we can see that the number is not even so we will try 3 next)
- 75 ÷ 3 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
- So our prime factors are ⇒ 300 = 2 x 2 x 3 x 5 x 5 or 2
^{2}x 3 x 5^{2 }

### If we want to check our answers on the calculator we can follow these steps:

- Type in your number, e.g. 130
- Press
- Then press
- You should see: