Solution: The GCF of 45 and 133 is 1
Methods
How to find the GCF of 45 and 133 using Prime Factorization
One way to find the GCF of 45 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 45?
What are the Factors of 133?
Here is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 5 1
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 45 and 133 is 1.
Thus, the GCF of 45 and 133 is: 1
How to Find the GCF of 45 and 133 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 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, 45 and 133:
Factors of 45: 1, 3, 5, 9, 15, 45
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 45 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 148 and 147?
What is the GCF of 115 and 84?
What is the GCF of 34 and 129?
What is the GCF of 136 and 39?
What is the GCF of 108 and 123?