Q:

What is the GCF of 24 and 117?

Accepted Solution

A:
Solution: The GCF of 24 and 117 is 3MethodsHow to find the GCF of 24 and 117 using Prime FactorizationOne way to find the GCF of 24 and 117 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 24?What are the Factors of 117?Here is the prime factorization of 24:23×312^3 × 3^123×31And this is the prime factorization of 117:32×1313^2 × 13^132×131When 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 24 and 117 by multiplying all the matching prime factors to get a GCF of 24 and 117 as 9:Thus, the GCF of 24 and 117 is: 9How to Find the GCF of 24 and 117 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 24 and 117 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, 24 and 117:Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors of 117: 1, 3, 9, 13, 39, 117When 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 24 and 117 would be 3.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 117 and 88?What is the GCF of 78 and 111?What is the GCF of 36 and 28?What is the GCF of 87 and 98?What is the GCF of 125 and 46?