Solution: The GCF of 74 and 113 is 1
Methods
How to find the GCF of 74 and 113 using Prime Factorization
One way to find the GCF of 74 and 113 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 74?
What are the Factors of 113?
Here is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 7 1
And this is the prime factorization of 113:
11
3
1
113^1
11 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 74 and 113 is 1.
Thus, the GCF of 74 and 113 is: 1
How to Find the GCF of 74 and 113 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 74 and 113 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, 74 and 113:
Factors of 74: 1, 2, 37, 74
Factors of 113: 1, 113
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 74 and 113 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 22 and 1?
What is the GCF of 83 and 19?
What is the GCF of 99 and 130?
What is the GCF of 70 and 71?
What is the GCF of 32 and 28?