Q:

What is the GCF of 125 and 112?

Accepted Solution

A:
Solution: The GCF of 125 and 112 is 1 Methods How to find the GCF of 125 and 112 using Prime Factorization One way to find the GCF of 125 and 112 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 125? What are the Factors of 112? Here is the prime factorization of 125: 5 3 5^3 5 3 And this is the prime factorization of 112: 2 4 × 7 1 2^4 × 7^1 2 4 × 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 125 and 112 is 1. Thus, the GCF of 125 and 112 is: 1 How to Find the GCF of 125 and 112 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 125 and 112 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, 125 and 112: Factors of 125: 1, 5, 25, 125 Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 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 125 and 112 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 38 and 100? What is the GCF of 59 and 111? What is the GCF of 2 and 107? What is the GCF of 29 and 114? What is the GCF of 98 and 42?