Solution: The GCF of 132 and 112 is 4
Methods
How to find the GCF of 132 and 112 using Prime Factorization
One way to find the GCF of 132 and 112 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 112?
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 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 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 112 by multiplying all the matching prime factors to get a GCF of 132 and 112 as 4:
Thus, the GCF of 132 and 112 is: 4
How to Find the GCF of 132 and 112 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 132 and 112 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 112:
Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
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 132 and 112 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 39 and 93?
What is the GCF of 134 and 129?
What is the GCF of 91 and 36?
What is the GCF of 146 and 116?
What is the GCF of 24 and 49?