Q:

What is the GCF of 30 and 82?

Accepted Solution

A:
Solution: The GCF of 30 and 82 is 2 Methods How to find the GCF of 30 and 82 using Prime Factorization One way to find the GCF of 30 and 82 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 30? What are the Factors of 82? Here is the prime factorization of 30: 2 1 × 3 1 × 5 1 2^1 × 3^1 × 5^1 2 1 × 3 1 × 5 1 And this is the prime factorization of 82: 2 1 × 4 1 1 2^1 × 41^1 2 1 × 4 1 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 30 and 82 by multiplying all the matching prime factors to get a GCF of 30 and 82 as 4: Thus, the GCF of 30 and 82 is: 4 How to Find the GCF of 30 and 82 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 30 and 82 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, 30 and 82: Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 82: 1, 2, 41, 82 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 30 and 82 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 79 and 129? What is the GCF of 68 and 134? What is the GCF of 142 and 137? What is the GCF of 78 and 19? What is the GCF of 118 and 140?