Solution: The GCF of 144 and 121 is 1
Methods
How to find the GCF of 144 and 121 using Prime Factorization
One way to find the GCF of 144 and 121 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 121?
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 121:
1
1
2
11^2
1 1 2
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 121 is 1.
Thus, the GCF of 144 and 121 is: 1
How to Find the GCF of 144 and 121 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 121 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 121:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 121: 1, 11, 121
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 121 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 39 and 53?
What is the GCF of 78 and 91?
What is the GCF of 105 and 14?
What is the GCF of 83 and 28?
What is the GCF of 66 and 120?