Q:

What is the GCF of 105 and 134?

Accepted Solution

A:
Solution: The GCF of 105 and 134 is 1 Methods How to find the GCF of 105 and 134 using Prime Factorization One way to find the GCF of 105 and 134 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 105? What are the Factors of 134? Here is the prime factorization of 105: 3 1 × 5 1 × 7 1 3^1 × 5^1 × 7^1 3 1 × 5 1 × 7 1 And this is the prime factorization of 134: 2 1 × 6 7 1 2^1 × 67^1 2 1 × 6 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 105 and 134 is 1. Thus, the GCF of 105 and 134 is: 1 How to Find the GCF of 105 and 134 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 105 and 134 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, 105 and 134: Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 Factors of 134: 1, 2, 67, 134 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 105 and 134 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 89 and 107? What is the GCF of 141 and 39? What is the GCF of 53 and 26? What is the GCF of 61 and 102? What is the GCF of 134 and 84?