Q:

What is the GCF of 13 and 104?

Accepted Solution

A:
Solution: The GCF of 13 and 104 is 13 Methods How to find the GCF of 13 and 104 using Prime Factorization One way to find the GCF of 13 and 104 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 13? What are the Factors of 104? Here is the prime factorization of 13: 1 3 1 13^1 1 3 1 And this is the prime factorization of 104: 2 3 × 1 3 1 2^3 × 13^1 2 3 × 1 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 13 and 104 by multiplying all the matching prime factors to get a GCF of 13 and 104 as 169: Thus, the GCF of 13 and 104 is: 169 How to Find the GCF of 13 and 104 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 13 and 104 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, 13 and 104: Factors of 13: 1, 13 Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104 When you compare the two lists of factors, you can see that the common factor(s) are 1, 13. Since 13 is the largest of these common factors, the GCF of 13 and 104 would be 13. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 39 and 36? What is the GCF of 53 and 37? What is the GCF of 28 and 69? What is the GCF of 106 and 24? What is the GCF of 119 and 88?