Solution: The GCF of 31 and 148 is 1
Methods
How to find the GCF of 31 and 148 using Prime Factorization
One way to find the GCF of 31 and 148 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 31?
What are the Factors of 148?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 148:
2
2
×
3
7
1
2^2 × 37^1
2 2 × 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 31 and 148 is 1.
Thus, the GCF of 31 and 148 is: 1
How to Find the GCF of 31 and 148 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 31 and 148 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, 31 and 148:
Factors of 31: 1, 31
Factors of 148: 1, 2, 4, 37, 74, 148
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 31 and 148 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 21 and 89?
What is the GCF of 73 and 62?
What is the GCF of 40 and 125?
What is the GCF of 85 and 11?
What is the GCF of 90 and 149?