MATH SOLVE

1 month ago

Q:
# What is the GCF of 130 and 113?

Accepted Solution

A:

Solution: The GCF of 130 and 113 is 1
Methods
How to find the GCF of 130 and 113 using Prime Factorization
One way to find the GCF of 130 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 130?
What are the Factors of 113?
Here is the prime factorization of 130:
2
1
×
5
1
×
1
3
1
2^1 × 5^1 × 13^1
2 1 × 5 1 × 1 3 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 130 and 113 is 1.
Thus, the GCF of 130 and 113 is: 1
How to Find the GCF of 130 and 113 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 130 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, 130 and 113:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
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 130 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 1 and 127?
What is the GCF of 65 and 83?
What is the GCF of 63 and 74?
What is the GCF of 56 and 9?
What is the GCF of 11 and 71?