Solution: The GCF of 12 and 144 is 12
Methods
How to find the GCF of 12 and 144 using Prime Factorization
One way to find the GCF of 12 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 12?
What are the Factors of 144?
Here is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 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 12 and 144 by multiplying all the matching prime factors to get a GCF of 12 and 144 as 36:
Thus, the GCF of 12 and 144 is: 36
How to Find the GCF of 12 and 144 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 12 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, 12 and 144:
Factors of 12: 1, 2, 3, 4, 6, 12
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, 3, 4, 6, 12. Since 12 is the largest of these common factors, the GCF of 12 and 144 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 57 and 26?
What is the GCF of 142 and 133?
What is the GCF of 128 and 22?
What is the GCF of 146 and 27?
What is the GCF of 47 and 62?