Q:

What is the GCF of 135 and 123?

Accepted Solution

A:
Solution: The GCF of 135 and 123 is 3MethodsHow to find the GCF of 135 and 123 using Prime FactorizationOne way to find the GCF of 135 and 123 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 123?Here is the prime factorization of 135:33×513^3 × 5^133×51And this is the prime factorization of 123:31×4113^1 × 41^131×411When 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 123 by multiplying all the matching prime factors to get a GCF of 135 and 123 as 9:Thus, the GCF of 135 and 123 is: 9How to Find the GCF of 135 and 123 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 135 and 123 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 123:Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135Factors of 123: 1, 3, 41, 123When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 135 and 123 would be 3.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 42 and 30?What is the GCF of 102 and 47?What is the GCF of 27 and 120?What is the GCF of 119 and 136?What is the GCF of 130 and 147?