Q:

What is the GCF of 32 and 58?

Accepted Solution

A:
Solution: The GCF of 32 and 58 is 2MethodsHow to find the GCF of 32 and 58 using Prime FactorizationOne way to find the GCF of 32 and 58 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 32?What are the Factors of 58?Here is the prime factorization of 32:252^525And this is the prime factorization of 58:21×2912^1 × 29^121×291When 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 32 and 58 by multiplying all the matching prime factors to get a GCF of 32 and 58 as 4:Thus, the GCF of 32 and 58 is: 4How to Find the GCF of 32 and 58 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 32 and 58 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, 32 and 58:Factors of 32: 1, 2, 4, 8, 16, 32Factors of 58: 1, 2, 29, 58When 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 32 and 58 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 5 and 17?What is the GCF of 55 and 141?What is the GCF of 144 and 65?What is the GCF of 118 and 62?What is the GCF of 109 and 29?