# Factor Tree Worksheets

Welcome to our Factor Tree Worksheets page.

Here you will find our selection of worksheets involving using factor trees for factorize numbers.

We have a range of sheets at different levels of difficulty.

## Factor Tree Worksheets

### What does a factor tree look like?

Let's have a look at a couple of examples.

Example 1) Complete the factor tree below and write down the prime factorization of 12. • The number in the top rectangle is the number we are trying to find the factors for.
• The numbers in the circles are the prime factors that multiply together to give the number above.
• The numbers in the other rectangles are composite (non-prime) numbers that we still need to find the factors for.

We know that 12 = 2 x 6 and 12 = 3 x 4 (we cannot use 1 in a factor tree!)

We can use either of these equations - it does not matter which one.

Let's use 12 = 2 x 6. So the prime factor is 2 and the composite factor is 6.

This gives us: Now we only have the 6 left to factorize.

We know that 6 = 1 x 6 and 6 = 2 x 3.

We cannot use 1 in a factor tree, so that leaves us with 6 = 2 x 3.

This gives us: The prime factors of 12 are 2, 2, and 3.

This means that 12 = 2 x 2 x 3 (or 22 x 3) as a product of prime factors (prime factorization.

Example 2) Let us go back to Example 1) and factorize it in a different way.

This time we will factorize 12 as 3 x 4 instead of 2 x 6.

This gives us: Now we only have the 4 left to factorize.

We know that 4 = 1 x 4 and 4 = 2 x 2.

We cannot use 1 in a factor tree, so that leaves us with 4 = 2 x 2.

This gives us: The prime factors of 12 are still 2, 2, and 3.

So we still end up with 12 = 2 x 2 x 3 (or 22 x 3) as a product of prime factors (prime factorization.

So we still have the same answer as Example 1) but the factor trees have some different numbers in.

The Factor Tree in Example 1) has a 6, and the Factor Tree in Example 2) has a 4.

This does not matter - the important thing is that the numbers in the circles (the prime factors) are the same in both examples.

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