Lesson 1: Prime Factorization6.NOS.4

I can…

I can write a number as a product of its prime factors using a factor tree.

Key words

• Prime number — A number bigger than 1 that you can only divide by 1 and itself.
• Composite number — A number bigger than 1 that you can divide by more than just 1 and itself.
• Prime factorization — Writing a number as prime numbers multiplied together.
• Factor tree — A picture that splits a number into its prime numbers, step by step.
• Exponent — A small number that tells how many times to multiply a number by itself.

Steps

1. I want the prime factorization of 60. I start by splitting it: 60 = 6 × 10.
2. 6 is not prime, so I break it: 6 = 2 × 3. Both 2 and 3 are prime, so I stop those branches.
3. 10 is not prime, so I break it: 10 = 2 × 5. Both 2 and 5 are prime, so I stop.
4. Now every factor is prime: 60 = 2 × 2 × 3 × 5.
5. Using exponents, I write it as 2² × 3 × 5. I check: 2 × 2 × 3 × 5 = 60. Correct.

Try it

What is the prime factorization of 40?

Check your answer

2 × 2 × 2 × 5

40 = 2 × 20 = 2 × 2 × 10 = 2 × 2 × 2 × 5. All factors (2, 2, 2, 5) are prime.

Sentence starter

I know ___ because ___.

Goal: I can explain how I broke a number down using the words prime number, composite number, factor, and exponent.