Q:

What is the GCF of 105 and 52?

Accepted Solution

A:
Solution: The GCF of 105 and 52 is 1 Methods How to find the GCF of 105 and 52 using Prime Factorization One way to find the GCF of 105 and 52 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 52? 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 52: 2 2 × 1 3 1 2^2 × 13^1 2 2 × 1 3 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 52 is 1. Thus, the GCF of 105 and 52 is: 1 How to Find the GCF of 105 and 52 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 105 and 52 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 52: Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 Factors of 52: 1, 2, 4, 13, 26, 52 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 52 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 138 and 42? What is the GCF of 109 and 101? What is the GCF of 100 and 140? What is the GCF of 32 and 76? What is the GCF of 120 and 145?