Q:

What is the GCF of 48 and 78?

Accepted Solution

A:
Solution: The GCF of 48 and 78 is 6 Methods How to find the GCF of 48 and 78 using Prime Factorization One way to find the GCF of 48 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 48? What are the Factors of 78? Here is the prime factorization of 48: 2 4 × 3 1 2^4 × 3^1 2 4 × 3 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 matching prime factors. You can now find the Greatest Common Factor of 48 and 78 by multiplying all the matching prime factors to get a GCF of 48 and 78 as 36: Thus, the GCF of 48 and 78 is: 36 How to Find the GCF of 48 and 78 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 48 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, 48 and 78: Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78 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 48 and 78 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 75 and 25? What is the GCF of 133 and 8? What is the GCF of 123 and 65? What is the GCF of 14 and 115? What is the GCF of 142 and 72?