Q:

What is the GCF of 43 and 86?

Accepted Solution

A:
Solution: The GCF of 43 and 86 is 43 Methods How to find the GCF of 43 and 86 using Prime Factorization One way to find the GCF of 43 and 86 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 43? What are the Factors of 86? Here is the prime factorization of 43: 4 3 1 43^1 4 3 1 And this is the prime factorization of 86: 2 1 × 4 3 1 2^1 × 43^1 2 1 × 4 3 1 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 43 and 86 by multiplying all the matching prime factors to get a GCF of 43 and 86 as 1849: Thus, the GCF of 43 and 86 is: 1849 How to Find the GCF of 43 and 86 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 43 and 86 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, 43 and 86: Factors of 43: 1, 43 Factors of 86: 1, 2, 43, 86 When you compare the two lists of factors, you can see that the common factor(s) are 1, 43. Since 43 is the largest of these common factors, the GCF of 43 and 86 would be 43. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 108 and 59? What is the GCF of 35 and 136? What is the GCF of 116 and 104? What is the GCF of 92 and 85? What is the GCF of 18 and 103?