Solution: The GCF of 144 and 60 is 12
Methods
How to find the GCF of 144 and 60 using Prime Factorization
One way to find the GCF of 144 and 60 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 144?
What are the Factors of 60?
Here is the prime factorization of 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
And this is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 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 144 and 60 by multiplying all the matching prime factors to get a GCF of 144 and 60 as 36:
Thus, the GCF of 144 and 60 is: 36
How to Find the GCF of 144 and 60 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 60 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, 144 and 60:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 12. Since 12 is the largest of these common factors, the GCF of 144 and 60 would be 12.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 132 and 145?
What is the GCF of 42 and 73?
What is the GCF of 27 and 2?
What is the GCF of 4 and 7?
What is the GCF of 143 and 15?