Solution: The GCF of 144 and 133 is 1
Methods
How to find the GCF of 144 and 133 using Prime Factorization
One way to find the GCF of 144 and 133 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 133?
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 133:
7
1
×
1
9
1
7^1 × 19^1
7 1 × 1 9 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 144 and 133 is 1.
Thus, the GCF of 144 and 133 is: 1
How to Find the GCF of 144 and 133 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 133 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 133:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 133: 1, 7, 19, 133
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 144 and 133 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 137 and 95?
What is the GCF of 58 and 114?
What is the GCF of 22 and 108?
What is the GCF of 63 and 15?
What is the GCF of 54 and 50?