Solution: The GCF of 77 and 110 is 11
Methods
How to find the GCF of 77 and 110 using Prime Factorization
One way to find the GCF of 77 and 110 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 77?
What are the Factors of 110?
Here is the prime factorization of 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 1 1 1
And this is the prime factorization of 110:
2
1
×
5
1
×
1
1
1
2^1 × 5^1 × 11^1
2 1 × 5 1 × 1 1 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 77 and 110 by multiplying all the matching prime factors to get a GCF of 77 and 110 as 121:
Thus, the GCF of 77 and 110 is: 121
How to Find the GCF of 77 and 110 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 77 and 110 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 77 and 110:
Factors of 77: 1, 7, 11, 77
Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
When you compare the two lists of factors, you can see that the common factor(s) are 1, 11. Since 11 is the largest of these common factors, the GCF of 77 and 110 would be 11.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 65 and 113?
What is the GCF of 88 and 57?
What is the GCF of 56 and 7?
What is the GCF of 124 and 59?
What is the GCF of 99 and 149?