Solution: The GCF of 36 and 132 is 12
Methods
How to find the GCF of 36 and 132 using Prime Factorization
One way to find the GCF of 36 and 132 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 36?
What are the Factors of 132?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
And this 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
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 36 and 132 by multiplying all the matching prime factors to get a GCF of 36 and 132 as 36:
Thus, the GCF of 36 and 132 is: 36
How to Find the GCF of 36 and 132 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 and 132 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, 36 and 132:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
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 36 and 132 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 90 and 109?
What is the GCF of 9 and 91?
What is the GCF of 23 and 140?
What is the GCF of 31 and 50?
What is the GCF of 102 and 56?