Q:

What is the GCF of 120 and 112?

Accepted Solution

A:
Solution: The GCF of 120 and 112 is 8MethodsHow to find the GCF of 120 and 112 using Prime FactorizationOne way to find the GCF of 120 and 112 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 120?What are the Factors of 112?Here is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51And this is the prime factorization of 112:24×712^4 × 7^124×71When 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 120 and 112 by multiplying all the matching prime factors to get a GCF of 120 and 112 as 4:Thus, the GCF of 120 and 112 is: 4How to Find the GCF of 120 and 112 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 120 and 112 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, 120 and 112:Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8. Since 8 is the largest of these common factors, the GCF of 120 and 112 would be 8.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 123 and 117?What is the GCF of 13 and 105?What is the GCF of 126 and 6?What is the GCF of 81 and 48?What is the GCF of 63 and 44?