LESSON 8 Prime Factors

Finding Prime Factors

Mrs. Dewey asked her class to write 24 as the product of at least three factors. Students had many different answers:

Which of these four ways show factors for 24 that are all prime?

The class noticed that all the factors Nicholas found were prime numbers. They are called the prime factors of 24. Nila found the same prime factors, but wrote them in a different order.

There are many ways to factor a number, but only one way (not counting the order in which they are written) in which all the factors are prime numbers. That means every whole number larger than 1 can be written as a product of prime numbers. For this reason, prime numbers are sometimes called the “building blocks of whole numbers.”

Nicholas showed how he found the prime factors of 24. He wrote: 24 = 3 8.

Then, he replaced the 8 with 4 2:
24 = 3 4 2.

Next, he replaced the 4 with 2 2:
24 = 3 2 2 2.

He stopped because none of the factors could be replaced. They were all prime.

When a number is written as a product of prime numbers, like 24 = 3 2 2 2, we have found its prime factorization.