Lesson 13: 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 Factorization — A number written as a product of primes.
• Prime number — A number over 1 that only splits by 1 and itself.
• Composite number — A number over 1 that is not prime.
• Factor — A number that goes into a number with none left.
• Factor tree — A picture that splits a number down to prime numbers.
• Exponent — A small raised number. It counts the times a number is used.

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

A family has 54 photos to sort into albums. What is the prime factorization of 54?

Check your answer

2 × 3 × 3 × 3

54 = 2 × 27 = 2 × 3 × 9 = 2 × 3 × 3 × 3. All factors (2, 3, 3, 3) 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.