Solution: The GCF of 132 and 110 is 22
Methods
How to find the GCF of 132 and 110 using Prime Factorization
One way to find the GCF of 132 and 110 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 110?
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 110:
2
1
×
5
1
×
1
1
1
2^1 × 5^1 × 11^1
2 1 × 5 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 132 and 110 by multiplying all the matching prime factors to get a GCF of 132 and 110 as 484:
Thus, the GCF of 132 and 110 is: 484
How to Find the GCF of 132 and 110 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 132 and 110 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 110:
Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 11, 22. Since 22 is the largest of these common factors, the GCF of 132 and 110 would be 22.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 20 and 83?
What is the GCF of 84 and 72?
What is the GCF of 145 and 86?
What is the GCF of 3 and 71?
What is the GCF of 9 and 111?