Q:

What is the GCF of 82 and 63?

Accepted Solution

A:
Solution: The GCF of 82 and 63 is 1 Methods How to find the GCF of 82 and 63 using Prime Factorization One way to find the GCF of 82 and 63 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 82? What are the Factors of 63? Here is the prime factorization of 82: 2 1 × 4 1 1 2^1 × 41^1 2 1 × 4 1 1 And this is the prime factorization of 63: 3 2 × 7 1 3^2 × 7^1 3 2 × 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 82 and 63 is 1. Thus, the GCF of 82 and 63 is: 1 How to Find the GCF of 82 and 63 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 82 and 63 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, 82 and 63: Factors of 82: 1, 2, 41, 82 Factors of 63: 1, 3, 7, 9, 21, 63 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 82 and 63 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 33 and 126? What is the GCF of 15 and 51? What is the GCF of 88 and 50? What is the GCF of 57 and 142? What is the GCF of 122 and 43?