Q:

What is the GCF of 78 and 84?

Accepted Solution

A:
Solution: The GCF of 78 and 84 is 6 Methods How to find the GCF of 78 and 84 using Prime Factorization One way to find the GCF of 78 and 84 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 84? 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 84: 2 2 × 3 1 × 7 1 2^2 × 3^1 × 7^1 2 2 × 3 1 × 7 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 84 by multiplying all the matching prime factors to get a GCF of 78 and 84 as 36: Thus, the GCF of 78 and 84 is: 36 How to Find the GCF of 78 and 84 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 78 and 84 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 84: Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 78 and 84 would be 6. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 117 and 4? What is the GCF of 1 and 129? What is the GCF of 28 and 8? What is the GCF of 58 and 26? What is the GCF of 74 and 110?