Solution: The GCF of 130 and 144 is 2
Methods
How to find the GCF of 130 and 144 using Prime Factorization
One way to find the GCF of 130 and 144 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 144?
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 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
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 144 by multiplying all the matching prime factors to get a GCF of 130 and 144 as 4:
Thus, the GCF of 130 and 144 is: 4
How to Find the GCF of 130 and 144 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 130 and 144 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 144:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 130 and 144 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 37 and 141?
What is the GCF of 104 and 1?
What is the GCF of 111 and 63?
What is the GCF of 72 and 49?
What is the GCF of 53 and 69?