Solution: The GCF of 45 and 134 is 1
Methods
How to find the GCF of 45 and 134 using Prime Factorization
One way to find the GCF of 45 and 134 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 134?
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 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 7 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 134 is 1.
Thus, the GCF of 45 and 134 is: 1
How to Find the GCF of 45 and 134 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 and 134 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 134:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 134: 1, 2, 67, 134
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 134 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 102 and 30?
What is the GCF of 105 and 82?
What is the GCF of 64 and 73?
What is the GCF of 38 and 100?
What is the GCF of 88 and 28?