Q:

What is the GCF of 100 and 120?

Accepted Solution

A:
Solution: The GCF of 100 and 120 is 20 Methods How to find the GCF of 100 and 120 using Prime Factorization One way to find the GCF of 100 and 120 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 100? What are the Factors of 120? Here is the prime factorization of 100: 2 2 × 5 2 2^2 × 5^2 2 2 × 5 2 And this is the prime factorization of 120: 2 3 × 3 1 × 5 1 2^3 × 3^1 × 5^1 2 3 × 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 100 and 120 by multiplying all the matching prime factors to get a GCF of 100 and 120 as 100: Thus, the GCF of 100 and 120 is: 100 How to Find the GCF of 100 and 120 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 100 and 120 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, 100 and 120: Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 5, 10, 20. Since 20 is the largest of these common factors, the GCF of 100 and 120 would be 20. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 46 and 84? What is the GCF of 147 and 91? What is the GCF of 109 and 38? What is the GCF of 103 and 78? What is the GCF of 134 and 104?