Solution: The GCF of 114 and 77 is 1
Methods
How to find the GCF of 114 and 77 using Prime Factorization
One way to find the GCF of 114 and 77 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 114?
What are the Factors of 77?
Here is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 9 1
And this is the prime factorization of 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 1 1 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 114 and 77 is 1.
Thus, the GCF of 114 and 77 is: 1
How to Find the GCF of 114 and 77 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 114 and 77 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, 114 and 77:
Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114
Factors of 77: 1, 7, 11, 77
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 114 and 77 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 23 and 6?
What is the GCF of 66 and 145?
What is the GCF of 148 and 57?
What is the GCF of 131 and 75?
What is the GCF of 62 and 26?