Solution: The GCF of 45 and 109 is 1
Methods
How to find the GCF of 45 and 109 using Prime Factorization
One way to find the GCF of 45 and 109 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 109?
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 109:
10
9
1
109^1
10 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 109 is 1.
Thus, the GCF of 45 and 109 is: 1
How to Find the GCF of 45 and 109 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 and 109 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 109:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 109: 1, 109
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 109 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 34 and 16?
What is the GCF of 112 and 73?
What is the GCF of 108 and 13?
What is the GCF of 123 and 87?
What is the GCF of 28 and 95?