Q:

What is the GCF of 135 and 120?

Accepted Solution

A:
Solution: The GCF of 135 and 120 is 15MethodsHow to find the GCF of 135 and 120 using Prime FactorizationOne way to find the GCF of 135 and 120 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 135?What are the Factors of 120?Here is the prime factorization of 135:33×513^3 × 5^133×51And this is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51When 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 135 and 120 by multiplying all the matching prime factors to get a GCF of 135 and 120 as 225:Thus, the GCF of 135 and 120 is: 225How to Find the GCF of 135 and 120 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 135 and 120 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, 135 and 120:Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 5, 15. Since 15 is the largest of these common factors, the GCF of 135 and 120 would be 15.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 106 and 41?What is the GCF of 48 and 22?What is the GCF of 11 and 27?What is the GCF of 115 and 108?What is the GCF of 36 and 74?