Solution: The GCF of 65 and 42 is 1
Methods
How to find the GCF of 65 and 42 using Prime Factorization
One way to find the GCF of 65 and 42 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 65?
What are the Factors of 42?
Here is the prime factorization of 65:
5
1
×
1
3
1
5^1 × 13^1
5 1 × 1 3 1
And this is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 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 65 and 42 is 1.
Thus, the GCF of 65 and 42 is: 1
How to Find the GCF of 65 and 42 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 65 and 42 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, 65 and 42:
Factors of 65: 1, 5, 13, 65
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
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 65 and 42 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 127 and 56?
What is the GCF of 90 and 66?
What is the GCF of 54 and 12?
What is the GCF of 79 and 131?
What is the GCF of 76 and 72?