Q:

What is the GCF of 65 and 51?

Accepted Solution

A:
Solution: The GCF of 65 and 51 is 1 Methods How to find the GCF of 65 and 51 using Prime Factorization One way to find the GCF of 65 and 51 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 51? 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 51: 3 1 × 1 7 1 3^1 × 17^1 3 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 65 and 51 is 1. Thus, the GCF of 65 and 51 is: 1 How to Find the GCF of 65 and 51 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 65 and 51 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 51: Factors of 65: 1, 5, 13, 65 Factors of 51: 1, 3, 17, 51 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 51 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 11 and 7? What is the GCF of 4 and 105? What is the GCF of 1 and 78? What is the GCF of 14 and 26? What is the GCF of 127 and 25?