What is a Greatest Common Factor, or GCF?

GCF stands for GREATEST COMMON FACTOR.

The GCF is commonly used to simplify or reduce fractions. These days, kids tend to use the words “simplify” or “simplest form.” When I was a student, we used “reduce.” They are the same thing, so be sure to use the terminology your children use at school to avoid frustration and confusion. Remember, it doesn’t matter how we did it when we were kids. What matters is that we learn to use our existing knowledge in the context of what our children are trying to accomplish.

Let’s say we have the fraction 6/18. We know by looking at 6/18 that it isn’t in simplest form (it’s not reduced). We wouldn’t go into a pizza shop and order 6/18 of a pizza, would we? No! We need to find the GCF in order to simplify 6/18.

Let’s factor both 6 and 18, and then find the greatest common factor.

6: 1,6,2,3

18: 1,18,2,9,3,6

The greatest common factor, or the factor that both 6 and 18 share, is 6. (Notice that 1, 2 and 3 are common, but they aren’t the GREATEST.)

Now, what do we do with our GCF of 6? Well, we divide the numerator (top #) by 6, and we divide the denominator (bottom #) by 6.

6 ÷ 6 = 1 (new numerator) 

18 ÷ 6 = 3 (new denominator)

So, 6/18 becomes 1/3. Now, you can go into the pizza shop and order 1/3 of a pizza!

Good luck!