Solution: The GCF of 12 and 108 is 12
Methods
How to find the GCF of 12 and 108 using Prime Factorization
One way to find the GCF of 12 and 108 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 12?
What are the Factors of 108?
Here is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 3 1
And this is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
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 12 and 108 by multiplying all the matching prime factors to get a GCF of 12 and 108 as 36:
Thus, the GCF of 12 and 108 is: 36
How to Find the GCF of 12 and 108 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 12 and 108 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, 12 and 108:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 12. Since 12 is the largest of these common factors, the GCF of 12 and 108 would be 12.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 15 and 45?
What is the GCF of 46 and 70?
What is the GCF of 58 and 56?
What is the GCF of 21 and 150?
What is the GCF of 10 and 139?