What is the Greatest Common Factor (GCF) of 77 and 264?
Are you on the hunt for the GCF of 77 and 264? 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 77 and 264?":
GCF of 77 and 264 = 11
What is the Greatest Common Factor?
- Greatest Common Denominator (GCD)
- Highest Common Factor (HCF)
- Greatest Common Divisor (GCD)
For most school problems or uses, you can look at the factors of the numbers and find the greatest common factor that way. For 77 and 264 those factors look like this:
- Factors for 77: 1, 7, 11, and 77
- Factors for 264: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, and 264
As you can see when you list out the factors of each number, 11 is the greatest number that 77 and 264 divides into.
List out all of the prime factors for each number:
- Prime Factors for 77: 7 and 11
- Prime Factors for 264: 2, 2, 2, 3, and 11
Now that we have the list of prime factors, we need to find any which are common for each number.
In this case, there is only one common prime factor, 11. Since there are no others, the greatest common factor is this prime factor:
GCF = 11
Find the GCF Using Euclid's Algorithm
The final method for calculating the GCF of 77 and 264 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.