Solution: The GCF of 112 and 106 is 2
Methods
How to find the GCF of 112 and 106 using Prime Factorization
One way to find the GCF of 112 and 106 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 106?
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 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 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 112 and 106 by multiplying all the matching prime factors to get a GCF of 112 and 106 as 4:
Thus, the GCF of 112 and 106 is: 4
How to Find the GCF of 112 and 106 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 112 and 106 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 106:
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 106: 1, 2, 53, 106
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 112 and 106 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 117 and 67?
What is the GCF of 26 and 5?
What is the GCF of 19 and 41?
What is the GCF of 121 and 91?
What is the GCF of 64 and 11?