Solution: The GCF of 30 and 131 is 1
Methods
How to find the GCF of 30 and 131 using Prime Factorization
One way to find the GCF of 30 and 131 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 30?
What are the Factors of 131?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 1
And this is the prime factorization of 131:
13
1
1
131^1
13 1 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 30 and 131 is 1.
Thus, the GCF of 30 and 131 is: 1
How to Find the GCF of 30 and 131 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 30 and 131 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, 30 and 131:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 131: 1, 131
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 30 and 131 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 111 and 137?
What is the GCF of 147 and 11?
What is the GCF of 141 and 40?
What is the GCF of 16 and 22?
What is the GCF of 50 and 133?