What is the unique factorization of composite numbers into prime factors?

Answer 1

Create a factor tree by doing this:

Choose your number. Let's pretend that it's 180.

Think of two things that multiply into that besides 1 and itself.

How about 18 and 10? Great!

On some paper, draw 180 with two lines coming downward out of it.

Write down 18 and 10.

Then think if any thing goes into 10 and 18.

5x2 and 9x2. Good ones.

Draw two lines coming out of 10 and out of 18 and write down: 5 and 2; 9 and 2.

Let's start with 10. 5 and 2 are prime numbers, so circle them.

Now for18. 2 is prime, so circle that, too.

However 9 is not prime, so draw two lines coming out of it and write down 3 and 3.

They are both prime, so circle them both. There is nothing left to factorize, so write down all of your circled numbers.

These are your prime factors. Bingo!