Q:

What is the GCF of 23 and 90?

Accepted Solution

A:
Solution: The GCF of 23 and 90 is 1 Methods How to find the GCF of 23 and 90 using Prime Factorization One way to find the GCF of 23 and 90 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 23? What are the Factors of 90? Here is the prime factorization of 23: 2 3 1 23^1 2 3 1 And this is the prime factorization of 90: 2 1 × 3 2 × 5 1 2^1 × 3^2 × 5^1 2 1 × 3 2 × 5 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 23 and 90 is 1. Thus, the GCF of 23 and 90 is: 1 How to Find the GCF of 23 and 90 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 23 and 90 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, 23 and 90: Factors of 23: 1, 23 Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 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 23 and 90 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 107 and 150? What is the GCF of 132 and 22? What is the GCF of 128 and 75? What is the GCF of 33 and 91? What is the GCF of 101 and 42?