Q:

What is the GCF of 58 and 64?

Accepted Solution

A:
Solution: The GCF of 58 and 64 is 2MethodsHow to find the GCF of 58 and 64 using Prime FactorizationOne way to find the GCF of 58 and 64 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 58?What are the Factors of 64?Here is the prime factorization of 58:21×2912^1 × 29^121×291And this is the prime factorization of 64:262^626When 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 58 and 64 by multiplying all the matching prime factors to get a GCF of 58 and 64 as 4:Thus, the GCF of 58 and 64 is: 4How to Find the GCF of 58 and 64 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 58 and 64 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, 58 and 64:Factors of 58: 1, 2, 29, 58Factors of 64: 1, 2, 4, 8, 16, 32, 64When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 58 and 64 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 105 and 18?What is the GCF of 21 and 24?What is the GCF of 19 and 38?What is the GCF of 93 and 119?What is the GCF of 140 and 111?