Q:

What is the GCF of 65 and 22?

Accepted Solution

A:
Solution: The GCF of 65 and 22 is 1 Methods How to find the GCF of 65 and 22 using Prime Factorization One way to find the GCF of 65 and 22 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 22? 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 22: 2 1 × 1 1 1 2^1 × 11^1 2 1 × 1 1 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 22 is 1. Thus, the GCF of 65 and 22 is: 1 How to Find the GCF of 65 and 22 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 65 and 22 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 22: Factors of 65: 1, 5, 13, 65 Factors of 22: 1, 2, 11, 22 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 22 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 136 and 148? What is the GCF of 39 and 51? What is the GCF of 73 and 15? What is the GCF of 103 and 92? What is the GCF of 83 and 22?