Q:

What is the GCF of 53 and 150?

Accepted Solution

A:
Solution: The GCF of 53 and 150 is 1 Methods How to find the GCF of 53 and 150 using Prime Factorization One way to find the GCF of 53 and 150 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 53? What are the Factors of 150? Here is the prime factorization of 53: 5 3 1 53^1 5 3 1 And this is the prime factorization of 150: 2 1 × 3 1 × 5 2 2^1 × 3^1 × 5^2 2 1 × 3 1 × 5 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 53 and 150 is 1. Thus, the GCF of 53 and 150 is: 1 How to Find the GCF of 53 and 150 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 53 and 150 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, 53 and 150: Factors of 53: 1, 53 Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 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 53 and 150 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 97 and 59? What is the GCF of 67 and 109? What is the GCF of 8 and 18? What is the GCF of 24 and 84? What is the GCF of 50 and 89?