Solution: The GCF of 52 and 117 is 13
Methods
How to find the GCF of 52 and 117 using Prime Factorization
One way to find the GCF of 52 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 52?
What are the Factors of 117?
Here is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 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 52 and 117 by multiplying all the matching prime factors to get a GCF of 52 and 117 as 169:
Thus, the GCF of 52 and 117 is: 169
How to Find the GCF of 52 and 117 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 52 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, 52 and 117:
Factors of 52: 1, 2, 4, 13, 26, 52
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, 13. Since 13 is the largest of these common factors, the GCF of 52 and 117 would be 13.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 55 and 33?
What is the GCF of 54 and 58?
What is the GCF of 80 and 114?
What is the GCF of 68 and 92?
What is the GCF of 104 and 145?