Solution: The GCF of 117 and 78 is 39
Methods
How to find the GCF of 117 and 78 using Prime Factorization
One way to find the GCF of 117 and 78 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 117?
What are the Factors of 78?
Here is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 1 3 1
And this is the prime factorization of 78:
2
1
×
3
1
×
1
3
1
2^1 × 3^1 × 13^1
2 1 × 3 1 × 1 3 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 117 and 78 by multiplying all the matching prime factors to get a GCF of 117 and 78 as 1521:
Thus, the GCF of 117 and 78 is: 1521
How to Find the GCF of 117 and 78 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 117 and 78 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, 117 and 78:
Factors of 117: 1, 3, 9, 13, 39, 117
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 13, 39. Since 39 is the largest of these common factors, the GCF of 117 and 78 would be 39.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 48 and 19?
What is the GCF of 23 and 58?
What is the GCF of 27 and 86?
What is the GCF of 129 and 135?
What is the GCF of 130 and 131?