Prime Factors

A prime factor is a factor of a number that is also a prime number

Here is an interesting property of prime numbers. Any number can be made by multiplying its prime factors together. Another way to say this is any number can be written as a product of its prime factors.

What are the prime factors of 36?

There is a technique to find all of the prime factors of a number called the factor tree method.

Start with 36 and find two of its factors that multiply together to make 36 like this

Then take these two factors and try and break them down into their factors.

12 has 4 and 3 as factors or 6 and 2 but 3 is a prime number and so can’t be broken down into its factors. Three is therefore, one of the prime factors of 36.

Let’s carry on breaking down 12 into its factors

Let’s choose 4 and 3 as the factors of 12 (we could have chosen 6 and 2 and we would get the same result).

3 is a prime number and so it is another prime factor of 36.

4 and be broken down into the factors 2 and 2

2 is a prime number. The prime factors of 36 are therefore 2, 2, 3 and 3. If we multiply these numbers together we get 36.

36 = 2 * 2 * 3 * 3