Solution: The GCF of 78 and 117 is 39
Methods
How to find the GCF of 78 and 117 using Prime Factorization
One way to find the GCF of 78 and 117 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 78?
What are the Factors of 117?
Here 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
And this is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 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 78 and 117 by multiplying all the matching prime factors to get a GCF of 78 and 117 as 1521:
Thus, the GCF of 78 and 117 is: 1521
How to Find the GCF of 78 and 117 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 78 and 117 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, 78 and 117:
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
Factors of 117: 1, 3, 9, 13, 39, 117
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 78 and 117 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 143?
What is the GCF of 134 and 92?
What is the GCF of 107 and 91?
What is the GCF of 54 and 21?
What is the GCF of 44 and 147?