Solution: The GCF of 18 and 17 is 1
Methods
How to find the GCF of 18 and 17 using Prime Factorization
One way to find the GCF of 18 and 17 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 18?
What are the Factors of 17?
Here is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
And this is the prime factorization of 17:
1
7
1
17^1
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 18 and 17 is 1.
Thus, the GCF of 18 and 17 is: 1
How to Find the GCF of 18 and 17 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 18 and 17 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, 18 and 17:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 17: 1, 17
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 18 and 17 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 15 and 98?
What is the GCF of 132 and 74?
What is the GCF of 123 and 146?
What is the GCF of 87 and 17?
What is the GCF of 31 and 82?