Solution: The GCF of 112 and 53 is 1
Methods
How to find the GCF of 112 and 53 using Prime Factorization
One way to find the GCF of 112 and 53 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 53?
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 53:
5
3
1
53^1
5 3 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 112 and 53 is 1.
Thus, the GCF of 112 and 53 is: 1
How to Find the GCF of 112 and 53 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 112 and 53 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 53:
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 53: 1, 53
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 112 and 53 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 42 and 2?
What is the GCF of 82 and 125?
What is the GCF of 134 and 55?
What is the GCF of 114 and 22?
What is the GCF of 69 and 103?