Solution: The GCF of 135 and 130 is 5
Methods
How to find the GCF of 135 and 130 using Prime Factorization
One way to find the GCF of 135 and 130 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 135?
What are the Factors of 130?
Here is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 1
And this 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
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 135 and 130 by multiplying all the matching prime factors to get a GCF of 135 and 130 as 25:
Thus, the GCF of 135 and 130 is: 25
How to Find the GCF of 135 and 130 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 135 and 130 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, 135 and 130:
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
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 135 and 130 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 36 and 125?
What is the GCF of 8 and 28?
What is the GCF of 96 and 23?
What is the GCF of 24 and 147?
What is the GCF of 119 and 62?