MATH SOLVE

1 month ago

Q:
# What is the GCF of 137 and 74?

Accepted Solution

A:

Solution: The GCF of 137 and 74 is 1
Methods
How to find the GCF of 137 and 74 using Prime Factorization
One way to find the GCF of 137 and 74 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 137?
What are the Factors of 74?
Here is the prime factorization of 137:
13
7
1
137^1
13 7 1
And this is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 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 137 and 74 is 1.
Thus, the GCF of 137 and 74 is: 1
How to Find the GCF of 137 and 74 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 137 and 74 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, 137 and 74:
Factors of 137: 1, 137
Factors of 74: 1, 2, 37, 74
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 137 and 74 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 82 and 96?
What is the GCF of 19 and 99?
What is the GCF of 132 and 33?
What is the GCF of 83 and 6?
What is the GCF of 25 and 120?