Q:

What is the GCF of 150 and 110?

Accepted Solution

A:
Solution: The GCF of 150 and 110 is 10 Methods How to find the GCF of 150 and 110 using Prime Factorization One way to find the GCF of 150 and 110 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 150? What are the Factors of 110? Here is the prime factorization of 150: 2 1 × 3 1 × 5 2 2^1 × 3^1 × 5^2 2 1 × 3 1 × 5 2 And this is the prime factorization of 110: 2 1 × 5 1 × 1 1 1 2^1 × 5^1 × 11^1 2 1 × 5 1 × 1 1 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 150 and 110 by multiplying all the matching prime factors to get a GCF of 150 and 110 as 100: Thus, the GCF of 150 and 110 is: 100 How to Find the GCF of 150 and 110 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 150 and 110 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, 150 and 110: Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 5, 10. Since 10 is the largest of these common factors, the GCF of 150 and 110 would be 10. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 70 and 108? What is the GCF of 44 and 125? What is the GCF of 81 and 61? What is the GCF of 116 and 98? What is the GCF of 149 and 115?