Solution: The GCF of 130 and 104 is 26
Methods
How to find the GCF of 130 and 104 using Prime Factorization
One way to find the GCF of 130 and 104 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 104?
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 104:
2
3
×
1
3
1
2^3 × 13^1
2 3 × 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 130 and 104 by multiplying all the matching prime factors to get a GCF of 130 and 104 as 676:
Thus, the GCF of 130 and 104 is: 676
How to Find the GCF of 130 and 104 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 130 and 104 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 104:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104
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 130 and 104 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 85 and 43?
What is the GCF of 114 and 47?
What is the GCF of 30 and 35?
What is the GCF of 143 and 76?
What is the GCF of 40 and 41?