Solution: The GCF of 130 and 125 is 5
Methods
How to find the GCF of 130 and 125 using Prime Factorization
One way to find the GCF of 130 and 125 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 125?
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 125:
5
3
5^3
5 3
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 130 and 125 by multiplying all the matching prime factors to get a GCF of 130 and 125 as 25:
Thus, the GCF of 130 and 125 is: 25
How to Find the GCF of 130 and 125 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 130 and 125 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 125:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
Factors of 125: 1, 5, 25, 125
When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 130 and 125 would be 5.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 119 and 144?
What is the GCF of 16 and 143?
What is the GCF of 63 and 11?
What is the GCF of 40 and 135?
What is the GCF of 109 and 92?