Solution: The GCF of 108 and 145 is 1
Methods
How to find the GCF of 108 and 145 using Prime Factorization
One way to find the GCF of 108 and 145 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 108?
What are the Factors of 145?
Here is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
And this is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 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 108 and 145 is 1.
Thus, the GCF of 108 and 145 is: 1
How to Find the GCF of 108 and 145 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 108 and 145 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, 108 and 145:
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 145: 1, 5, 29, 145
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 108 and 145 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 96 and 83?
What is the GCF of 138 and 84?
What is the GCF of 27 and 42?
What is the GCF of 110 and 100?
What is the GCF of 112 and 75?