Q:

What is the GCF of 118 and 64?

Accepted Solution

A:
Solution: The GCF of 118 and 64 is 2 Methods How to find the GCF of 118 and 64 using Prime Factorization One way to find the GCF of 118 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 118? What are the Factors of 64? Here is the prime factorization of 118: 2 1 × 5 9 1 2^1 × 59^1 2 1 × 5 9 1 And this is the prime factorization of 64: 2 6 2^6 2 6 When 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 118 and 64 by multiplying all the matching prime factors to get a GCF of 118 and 64 as 4: Thus, the GCF of 118 and 64 is: 4 How to Find the GCF of 118 and 64 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 118 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, 118 and 64: Factors of 118: 1, 2, 59, 118 Factors of 64: 1, 2, 4, 8, 16, 32, 64 When 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 118 and 64 would be 2. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 122 and 66? What is the GCF of 56 and 33? What is the GCF of 145 and 10? What is the GCF of 141 and 149? What is the GCF of 9 and 115?