Solution: The GCF of 108 and 116 is 4
Methods
How to find the GCF of 108 and 116 using Prime Factorization
One way to find the GCF of 108 and 116 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 108?
What are the Factors of 116?
Here is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 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 108 and 116 by multiplying all the matching prime factors to get a GCF of 108 and 116 as 4:
Thus, the GCF of 108 and 116 is: 4
How to Find the GCF of 108 and 116 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 108 and 116 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, 108 and 116:
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 116: 1, 2, 4, 29, 58, 116
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 108 and 116 would be 4.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 48 and 28?
What is the GCF of 89 and 64?
What is the GCF of 129 and 103?
What is the GCF of 73 and 143?
What is the GCF of 145 and 18?