Q:

What is the GCF of 146 and 135?

Accepted Solution

A:
Solution: The GCF of 146 and 135 is 1 Methods How to find the GCF of 146 and 135 using Prime Factorization One way to find the GCF of 146 and 135 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 146? What are the Factors of 135? Here is the prime factorization of 146: 2 1 × 7 3 1 2^1 × 73^1 2 1 × 7 3 1 And this is the prime factorization of 135: 3 3 × 5 1 3^3 × 5^1 3 3 × 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 146 and 135 is 1. Thus, the GCF of 146 and 135 is: 1 How to Find the GCF of 146 and 135 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 146 and 135 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, 146 and 135: Factors of 146: 1, 2, 73, 146 Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135 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 146 and 135 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 50 and 141? What is the GCF of 120 and 78? What is the GCF of 61 and 119? What is the GCF of 103 and 117? What is the GCF of 111 and 14?