Solution: The GCF of 45 and 2 is 1
Methods
How to find the GCF of 45 and 2 using Prime Factorization
One way to find the GCF of 45 and 2 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 2?
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 2:
2
1
2^1
2 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 2 is 1.
Thus, the GCF of 45 and 2 is: 1
How to Find the GCF of 45 and 2 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 and 2 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 2:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 2: 1, 2
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 2 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 116 and 136?
What is the GCF of 14 and 29?
What is the GCF of 80 and 47?
What is the GCF of 101 and 115?
What is the GCF of 15 and 30?