Solution: The GCF of 85 and 112 is 1
Methods
How to find the GCF of 85 and 112 using Prime Factorization
One way to find the GCF of 85 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 85?
What are the Factors of 112?
Here is the prime factorization of 85:
5
1
×
1
7
1
5^1 × 17^1
5 1 × 1 7 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 no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 85 and 112 is 1.
Thus, the GCF of 85 and 112 is: 1
How to Find the GCF of 85 and 112 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 85 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, 85 and 112:
Factors of 85: 1, 5, 17, 85
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 only common factor is 1. So, in this case, the GCF of 85 and 112 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 66 and 5?
What is the GCF of 122 and 112?
What is the GCF of 129 and 70?
What is the GCF of 115 and 118?
What is the GCF of 105 and 75?