Solution: The GCF of 61 and 18 is 1
Methods
How to find the GCF of 61 and 18 using Prime Factorization
One way to find the GCF of 61 and 18 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 61?
What are the Factors of 18?
Here is the prime factorization of 61:
6
1
1
61^1
6 1 1
And this is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
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 61 and 18 is 1.
Thus, the GCF of 61 and 18 is: 1
How to Find the GCF of 61 and 18 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 61 and 18 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, 61 and 18:
Factors of 61: 1, 61
Factors of 18: 1, 2, 3, 6, 9, 18
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 61 and 18 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 64 and 116?
What is the GCF of 105 and 30?
What is the GCF of 18 and 53?
What is the GCF of 112 and 77?
What is the GCF of 110 and 28?