Q:

What is the GCF of 64 and 36?

Accepted Solution

A:
Solution: The GCF of 64 and 36 is 4MethodsHow to find the GCF of 64 and 36 using Prime FactorizationOne way to find the GCF of 64 and 36 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 64?What are the Factors of 36?Here is the prime factorization of 64:262^626And this is the prime factorization of 36:22×322^2 × 3^222×32When 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 64 and 36 by multiplying all the matching prime factors to get a GCF of 64 and 36 as 4:Thus, the GCF of 64 and 36 is: 4How to Find the GCF of 64 and 36 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 64 and 36 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, 64 and 36:Factors of 64: 1, 2, 4, 8, 16, 32, 64Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 64 and 36 would be 4.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 102 and 54?What is the GCF of 77 and 139?What is the GCF of 98 and 149?What is the GCF of 31 and 27?What is the GCF of 23 and 101?