Find the common factors of 56 and 36 and state the GCF.
So we want to find the common factors, and then we also want to find the GCF, the greatest common factor. But to do so, we must understand what a factor is. Factors are numbers that multiply to give us a specific number. For this example, that’s 56 and also 36. So another way to think about that would be numbers that divide evenly into 56 and evenly into 36.
So to find the factors of 56, let’s write down the numbers that multiply together to give us 56. One times 56 is equal to 56. Two times 28 is equal to 56. Four times 14 is equal to 56. And seven times eight is equal to 56. So to list these factors, these numbers that multiply to be 56 or we could think these numbers that divide evenly into 56, let’s list them from least to greatest: one, two, four, seven, eight, 14, 28, and 56. So these are all of the factors of 56.
So to find the factors of 36, let’s look at all the numbers that multiply together to be 36. One times 36 equals 36. Two times 18 equals 36. Four times nine equals 36. And six times six equals 36. So let’s list this out in increasing order: one, two, four, six, which we only have to list once, nine, 18, and 36. So what factors do they have in common?
They both have one. They both have two. They both have four. And then after that, they actually don’t have any factors in common. So the only common factors they have are one, two, and four. So out of those, what is our greatest common factor?
Well out of one, two, and four, four the greatest. So our GCF is equal to four. So a GCF, we can think of what is the greatest number, the biggest number, that can go into evenly 56 and 36. And right now, we have that that is four. So once again, the common factors are one, two, and four, and the GCF is equal to four.