Solution: The GCF of 45 and 14 is 1
Methods
How to find the GCF of 45 and 14 using Prime Factorization
One way to find the GCF of 45 and 14 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 14?
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 14:
2
1
×
7
1
2^1 × 7^1
2 1 × 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 14 is 1.
Thus, the GCF of 45 and 14 is: 1
How to Find the GCF of 45 and 14 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 and 14 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 14:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 14: 1, 2, 7, 14
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 14 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 141 and 130?
What is the GCF of 80 and 23?
What is the GCF of 72 and 138?
What is the GCF of 104 and 108?
What is the GCF of 49 and 66?