# Prime factors

We know Prime `=` Prime numbers 2, 3, 5, 7, 11, 13.............

We know Factors `=` Take a number apart using ladders

So logically Prime Factors are:

**Example 1**

What is the prime factorization of 12?

Factor the number 12

Write down the number and put two ladders up against it.

Then write the numbers from 1 down the left ladder.

Now fill the right ladder with the numbers that multiply to give 12.

Therefore the factors of 12 are:

1 and 12

2 and 6

3 and 4

Alternatively the factors of 12 are 1, 2, 3, 4, 6 and 12

The only prime numbers that are also factors of 12 are:

2 and 3

So we have to use only these two numbers to multiply to 12.

Try `2times3=6`

Try `(2times3=6)times2=12`

So the answer is `2times3times2`

or `2times2times3`

or `2^2times3`

**Example 2**

What are the prime factors of 24?

The only prime numbers that are also factors of 24 are:

`2` and `3`

So we have to use only these two numbers to multiply to 24.

Try `2times3=6`

Try `(2times3=6)times3=18` - can't multiply to get 24

Try `(2times3=6)times2=12`

Try `(2times3times2=12)times2=24`

So the answer is `2times3times2times2`

which is `2times2times2times3`

or `2^3times3`

**Example 3**

What is the prime factorisation of 70?

Factor 70

The only prime numbers that are also factors of 70 are:

2, 5 and 7

So we have to use only these 3 numbers to multiply to 70

Try `2times5=10`

Try `(2times5=10)times7=70`

So the answer is `2times5times7`

**Example 4**

What is the prime factorisation of 147?

Factor 147

**NOTE:**

21 and 49 are not prime numbers.

The only prime numbers that are also factors of 147 are:

3 and 7

So we have to use only these two numbers to multiply to 147.

Try `3times7=21`

Try `(3times7=21)times7=147`

So the answer is `3times7times7`

or ` 3times7^2`

**Example 5**

What is the prime factorisation of 17?

Factor 17

There are no other combinations that work.

17 is a prime number.

So 17 is the prime factorisation.