Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 4: Factors and Multiples 51

Let’s look at the prime factorization of 180 as an example. Start with any pair of factors of 180
that you can recall, maybe 18 and 10. Put 180 at the top of the tree and make a branch for 18 and
a branch for 10.

Focus on the 18 branch. Can you find factors for 18? 2 and 9 will work. Add them as branches
under 18.

Is 2 a prime? Yes, so mark it with a circle or a box. That branch is done. Is 9 prime? No, but it
factors to 3 v 3, and 3 is prime. The tree needs branches under the nine.

When that branch is down to primes, turn to the 10 branch. 10 = 2 v 5, and both of those
numbers are prime.

Collect all the primes you marked and you have the prime factorization of 180.
180 = 2 v 2 v 3 v 3 v 5.

18

180

10

18

29

180

10

18

29

180

10

3 3

18

29

180

10

3 3

2 5

CHECK POINT

Use a factor tree to help you find the prime factorization of each number.

6. 78


7. 98


8. 189

9. 255

10. 512