Q:

What is the GCF of 24 and 144?

Accepted Solution

A:
Solution: The GCF of 24 and 144 is 24MethodsHow to find the GCF of 24 and 144 using Prime FactorizationOne way to find the GCF of 24 and 144 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 144?Here is the prime factorization of 24:23×312^3 × 3^123×31And this is the prime factorization of 144:24×322^4 × 3^224×32When 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 144 by multiplying all the matching prime factors to get a GCF of 24 and 144 as 36:Thus, the GCF of 24 and 144 is: 36How to Find the GCF of 24 and 144 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 24 and 144 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 144:Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 8, 12, 24. Since 24 is the largest of these common factors, the GCF of 24 and 144 would be 24.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 117 and 95?What is the GCF of 88 and 43?What is the GCF of 12 and 102?What is the GCF of 106 and 47?What is the GCF of 130 and 13?