Q:

What is the GCF of 90 and 15?

Accepted Solution

A:
Solution: The GCF of 90 and 15 is 15 Methods How to find the GCF of 90 and 15 using Prime Factorization One way to find the GCF of 90 and 15 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 90? What are the Factors of 15? Here is the prime factorization of 90: 2 1 × 3 2 × 5 1 2^1 × 3^2 × 5^1 2 1 × 3 2 × 5 1 And this is the prime factorization of 15: 3 1 × 5 1 3^1 × 5^1 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 90 and 15 by multiplying all the matching prime factors to get a GCF of 90 and 15 as 225: Thus, the GCF of 90 and 15 is: 225 How to Find the GCF of 90 and 15 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 90 and 15 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, 90 and 15: Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 Factors of 15: 1, 3, 5, 15 When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 5, 15. Since 15 is the largest of these common factors, the GCF of 90 and 15 would be 15. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 13 and 22? What is the GCF of 34 and 21? What is the GCF of 106 and 101? What is the GCF of 29 and 12? What is the GCF of 123 and 125?