Q:

What is the GCF of 80 and 145?

Accepted Solution

A:
Solution: The GCF of 80 and 145 is 5 Methods How to find the GCF of 80 and 145 using Prime Factorization One way to find the GCF of 80 and 145 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 80? What are the Factors of 145? Here is the prime factorization of 80: 2 4 × 5 1 2^4 × 5^1 2 4 × 5 1 And this is the prime factorization of 145: 5 1 × 2 9 1 5^1 × 29^1 5 1 × 2 9 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 80 and 145 by multiplying all the matching prime factors to get a GCF of 80 and 145 as 25: Thus, the GCF of 80 and 145 is: 25 How to Find the GCF of 80 and 145 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 80 and 145 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, 80 and 145: Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Factors of 145: 1, 5, 29, 145 When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 80 and 145 would be 5. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 65 and 62? What is the GCF of 100 and 94? What is the GCF of 76 and 122? What is the GCF of 21 and 61? What is the GCF of 34 and 72?