Q:

What is the GCF of 78 and 65?

Accepted Solution

A:
Solution: The GCF of 78 and 65 is 13 Methods How to find the GCF of 78 and 65 using Prime Factorization One way to find the GCF of 78 and 65 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 78? What are the Factors of 65? Here 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 And this is the prime factorization of 65: 5 1 × 1 3 1 5^1 × 13^1 5 1 × 1 3 1 When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 78 and 65 by multiplying all the matching prime factors to get a GCF of 78 and 65 as 169: Thus, the GCF of 78 and 65 is: 169 How to Find the GCF of 78 and 65 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 78 and 65 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, 78 and 65: Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78 Factors of 65: 1, 5, 13, 65 When you compare the two lists of factors, you can see that the common factor(s) are 1, 13. Since 13 is the largest of these common factors, the GCF of 78 and 65 would be 13. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 95 and 150? What is the GCF of 147 and 66? What is the GCF of 118 and 6? What is the GCF of 59 and 43? What is the GCF of 27 and 5?