Solution: The GCF of 67 and 76 is 1
Methods
How to find the GCF of 67 and 76 using Prime Factorization
One way to find the GCF of 67 and 76 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 67?
What are the Factors of 76?
Here is the prime factorization of 67:
6
7
1
67^1
6 7 1
And this is the prime factorization of 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 9 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 67 and 76 is 1.
Thus, the GCF of 67 and 76 is: 1
How to Find the GCF of 67 and 76 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 67 and 76 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, 67 and 76:
Factors of 67: 1, 67
Factors of 76: 1, 2, 4, 19, 38, 76
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 67 and 76 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 69 and 106?
What is the GCF of 108 and 15?
What is the GCF of 126 and 25?
What is the GCF of 88 and 144?
What is the GCF of 138 and 39?