Solution: The GCF of 52 and 130 is 26
Methods
How to find the GCF of 52 and 130 using Prime Factorization
One way to find the GCF of 52 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 52?
What are the Factors of 130?
Here is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 1 3 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 52 and 130 by multiplying all the matching prime factors to get a GCF of 52 and 130 as 676:
Thus, the GCF of 52 and 130 is: 676
How to Find the GCF of 52 and 130 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 52 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, 52 and 130:
Factors of 52: 1, 2, 4, 13, 26, 52
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, 2, 13, 26. Since 26 is the largest of these common factors, the GCF of 52 and 130 would be 26.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 1 and 95?
What is the GCF of 58 and 39?
What is the GCF of 46 and 44?
What is the GCF of 28 and 10?
What is the GCF of 66 and 99?