Q:

What is the GCF of 150 and 22?

Accepted Solution

A:
Solution: The GCF of 150 and 22 is 2MethodsHow to find the GCF of 150 and 22 using Prime FactorizationOne way to find the GCF of 150 and 22 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 22?Here is the prime factorization of 150:21×31×522^1 × 3^1 × 5^221×31×52And this is the prime factorization of 22:21×1112^1 × 11^121×111When 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 22 by multiplying all the matching prime factors to get a GCF of 150 and 22 as 4:Thus, the GCF of 150 and 22 is: 4How to Find the GCF of 150 and 22 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 150 and 22 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 22:Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150Factors of 22: 1, 2, 11, 22When 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 150 and 22 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 12 and 122?What is the GCF of 125 and 114?What is the GCF of 98 and 3?What is the GCF of 112 and 58?What is the GCF of 5 and 103?