Q:

What is the GCF of 76 and 150?

Accepted Solution

A:
Solution: The GCF of 76 and 150 is 2 Methods How to find the GCF of 76 and 150 using Prime Factorization One way to find the GCF of 76 and 150 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 76? What are the Factors of 150? Here is the prime factorization of 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 9 1 And this is the prime factorization of 150: 2 1 × 3 1 × 5 2 2^1 × 3^1 × 5^2 2 1 × 3 1 × 5 2 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 76 and 150 by multiplying all the matching prime factors to get a GCF of 76 and 150 as 4: Thus, the GCF of 76 and 150 is: 4 How to Find the GCF of 76 and 150 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 76 and 150 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, 76 and 150: Factors of 76: 1, 2, 4, 19, 38, 76 Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 76 and 150 would be 2. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 5 and 150? What is the GCF of 69 and 33? What is the GCF of 92 and 127? What is the GCF of 41 and 31? What is the GCF of 86 and 137?