Q:

What is the GCF of 104 and 30?

Accepted Solution

A:
Solution: The GCF of 104 and 30 is 2 Methods How to find the GCF of 104 and 30 using Prime Factorization One way to find the GCF of 104 and 30 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 104? What are the Factors of 30? Here is the prime factorization of 104: 2 3 × 1 3 1 2^3 × 13^1 2 3 × 1 3 1 And this is the prime factorization of 30: 2 1 × 3 1 × 5 1 2^1 × 3^1 × 5^1 2 1 × 3 1 × 5 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 104 and 30 by multiplying all the matching prime factors to get a GCF of 104 and 30 as 4: Thus, the GCF of 104 and 30 is: 4 How to Find the GCF of 104 and 30 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 104 and 30 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, 104 and 30: Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 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 104 and 30 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 13 and 107? What is the GCF of 141 and 133? What is the GCF of 43 and 106? What is the GCF of 136 and 119? What is the GCF of 99 and 135?