What is the Greatest Common Factor (GCF) of 76 and 646?

Are you on the hunt for the GCF of 76 and 646? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!

First off, if you're in a rush, here's the answer to the question "what is the GCF of 76 and 646?":

GCF of 76 and 646 = 38

What is the Greatest Common Factor?

Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:

  • Greatest Common Denominator (GCD)
  • Highest Common Factor (HCF)
  • Greatest Common Divisor (GCD)

There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.

For most school problems or uses, you can look at the factors of the numbers and find the greatest common factor that way. For 76 and 646 those factors look like this:

  • Factors for 76: 1, 2, 4, 19, 38, and 76
  • Factors for 646: 1, 2, 17, 19, 34, 38, 323, and 646

As you can see when you list out the factors of each number, 38 is the greatest number that 76 and 646 divides into.

Prime Factors

As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.

List out all of the prime factors for each number:

  • Prime Factors for 76: 2, 2, and 19
  • Prime Factors for 646: 2, 17, and 19

Now that we have the list of prime factors, we need to find any which are common for each number.

Looking at the occurences of common prime factors in 76 and 646 we can see that the commonly occuring prime factors are 2 and 19.

To calculate the prime factor, we multiply these numbers together:

GCF = 2 x 19 = 38

Find the GCF Using Euclid's Algorithm

The final method for calculating the GCF of 76 and 646 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.

If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page.

Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. Grab a pencil and paper and give it a try for yourself. (or just use our GCD calculator - we won't tell anyone!)