Solution: The GCF of 132 and 84 is 12
Methods
How to find the GCF of 132 and 84 using Prime Factorization
One way to find the GCF of 132 and 84 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 132?
What are the Factors of 84?
Here is the prime factorization of 132:
2
2
×
3
1
×
1
1
1
2^2 × 3^1 × 11^1
2 2 × 3 1 × 1 1 1
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 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 132 and 84 by multiplying all the matching prime factors to get a GCF of 132 and 84 as 36:
Thus, the GCF of 132 and 84 is: 36
How to Find the GCF of 132 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 132 and 84 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, 132 and 84:
Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 132 and 84 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 14 and 61?
What is the GCF of 142 and 92?
What is the GCF of 57 and 145?
What is the GCF of 46 and 67?
What is the GCF of 118 and 130?