Q:

What is the GCF of 35 and 78?

Accepted Solution

A:
Solution: The GCF of 35 and 78 is 1 Methods How to find the GCF of 35 and 78 using Prime Factorization One way to find the GCF of 35 and 78 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 35? What are the Factors of 78? Here is the prime factorization of 35: 5 1 × 7 1 5^1 × 7^1 5 1 × 7 1 And this is the prime factorization of 78: 2 1 × 3 1 × 1 3 1 2^1 × 3^1 × 13^1 2 1 × 3 1 × 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 35 and 78 is 1. Thus, the GCF of 35 and 78 is: 1 How to Find the GCF of 35 and 78 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 35 and 78 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, 35 and 78: Factors of 35: 1, 5, 7, 35 Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78 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 35 and 78 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 110 and 15? What is the GCF of 48 and 36? What is the GCF of 93 and 50? What is the GCF of 142 and 13? What is the GCF of 131 and 126?