Q:

What is the GCF of 78 and 104?

Accepted Solution

A:
Solution: The GCF of 78 and 104 is 26 Methods How to find the GCF of 78 and 104 using Prime Factorization One way to find the GCF of 78 and 104 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 104? 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 104: 2 3 × 1 3 1 2^3 × 13^1 2 3 × 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 104 by multiplying all the matching prime factors to get a GCF of 78 and 104 as 676: Thus, the GCF of 78 and 104 is: 676 How to Find the GCF of 78 and 104 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 78 and 104 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 104: Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78 Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 13, 26. Since 26 is the largest of these common factors, the GCF of 78 and 104 would be 26. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 35 and 17? What is the GCF of 74 and 13? What is the GCF of 43 and 87? What is the GCF of 119 and 6? What is the GCF of 31 and 62?