Math 7 · Unit 4, Lesson 4: Factoring Out the GCF · Tile 1 of 3
The Greatest Common Factor
The biggest number that goes into all of them
The biggest number that goes into all of them
The greatest common factor, or GCF, is the biggest number that divides into every number evenly. Here's a fast way to find it. List the factors of the smallest number, biggest first. Stop at the first one that also goes into all the others.
Words we use
| Elle (math-speak) | Finn (plain English) |
|---|---|
| Common | Shared by everyone. Common ground is ground that everybody shares. |
| Greatest common factor | The biggest number that goes into every one of the numbers, with nothing left over. GCF for short. |
Elle and Finn
The greatest common factor of two or more whole numbers is the largest whole number that divides each of them.
Find the biggest number that fits into all of them evenly. That's the one you pull out.
Watch it work
List the factors of the smallest number from biggest to smallest, and cross out the ones that fail.
When the GCF is 1, there is nothing useful to pull out.
The GCF of the terms 12x and 18 is 6. Use only the numbers. In 7th grade we pull out a number, never the variable.
NC standard: NC.7.EE.1.