Q:

What is the GCF of 75 and 90?

Accepted Solution

A:
Solution: The GCF of 75 and 90 is 15 Methods How to find the GCF of 75 and 90 using Prime Factorization One way to find the GCF of 75 and 90 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 75? What are the Factors of 90? Here is the prime factorization of 75: 3 1 × 5 2 3^1 × 5^2 3 1 × 5 2 And this is the prime factorization of 90: 2 1 × 3 2 × 5 1 2^1 × 3^2 × 5^1 2 1 × 3 2 × 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 75 and 90 by multiplying all the matching prime factors to get a GCF of 75 and 90 as 225: Thus, the GCF of 75 and 90 is: 225 How to Find the GCF of 75 and 90 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 75 and 90 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, 75 and 90: Factors of 75: 1, 3, 5, 15, 25, 75 Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 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 75 and 90 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 140 and 121? What is the GCF of 124 and 94? What is the GCF of 57 and 128? What is the GCF of 129 and 115? What is the GCF of 73 and 26?