Q:

What is the GCF of 132 and 29?

Accepted Solution

A:
Solution: The GCF of 132 and 29 is 1 Methods How to find the GCF of 132 and 29 using Prime Factorization One way to find the GCF of 132 and 29 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 132? What are the Factors of 29? Here is the prime factorization of 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 1 1 And this is the prime factorization of 29: 2 9 1 29^1 2 9 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 132 and 29 is 1. Thus, the GCF of 132 and 29 is: 1 How to Find the GCF of 132 and 29 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 132 and 29 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, 132 and 29: Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 Factors of 29: 1, 29 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 132 and 29 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 26 and 83? What is the GCF of 118 and 100? What is the GCF of 114 and 30? What is the GCF of 136 and 97? What is the GCF of 48 and 113?