Solution: The GCF of 112 and 32 is 16
Methods
How to find the GCF of 112 and 32 using Prime Factorization
One way to find the GCF of 112 and 32 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 112?
What are the Factors of 32?
Here is the prime factorization of 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 7 1
And this is the prime factorization of 32:
2
5
2^5
2 5
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 112 and 32 by multiplying all the matching prime factors to get a GCF of 112 and 32 as 4:
Thus, the GCF of 112 and 32 is: 4
How to Find the GCF of 112 and 32 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 112 and 32 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, 112 and 32:
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 32: 1, 2, 4, 8, 16, 32
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8, 16. Since 16 is the largest of these common factors, the GCF of 112 and 32 would be 16.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 70 and 66?
What is the GCF of 99 and 45?
What is the GCF of 89 and 111?
What is the GCF of 13 and 19?
What is the GCF of 75 and 98?