Lesson 2: Greatest Common Factor6.NOS.4

I can…

I can find the greatest common factor (GCF) of two numbers by listing or comparing their factors.

Key words

• Factor — A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
• Greatest Common Factor — The biggest number that divides two or more numbers evenly.
• Common factor — A number that divides two or more numbers evenly.
• Divisible — A number you can divide evenly, with nothing left over.
• Prime factorization — Writing a number as prime numbers multiplied together. It helps you find the GCF.

Steps

1. I want the GCF of 24 and 36. First I list the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
2. Next I list the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
3. Now I circle the factors in BOTH lists: 1, 2, 3, 4, 6, 12. These are the common factors.
4. The biggest one is 12, so the GCF of 24 and 36 is 12. I check: 24 ÷ 12 = 2 and 36 ÷ 12 = 3. Both are even, so 12 works.

Try it

What is the GCF of 18 and 27?

Check your answer

9

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The factors they share are 1, 3, and 9, so the GCF is 9 — the GREATEST shared factor, not just any common factor (that rules out 3). Six divides 18 but not 27, so it is not actually a common factor at all, and 18 is one of the original numbers, not a factor shared with 27.

Sentence starter

I know ___ because ___.

Goal: I can explain how I found the GCF using the words factor, common factor, divisible, and greatest common factor.