Q:

What is the GCF of 75 and 147?

Accepted Solution

A:
Solution: The GCF of 75 and 147 is 3 Methods How to find the GCF of 75 and 147 using Prime Factorization One way to find the GCF of 75 and 147 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 147? 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 147: 3 1 × 7 2 3^1 × 7^2 3 1 × 7 2 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 147 by multiplying all the matching prime factors to get a GCF of 75 and 147 as 9: Thus, the GCF of 75 and 147 is: 9 How to Find the GCF of 75 and 147 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 75 and 147 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 147: Factors of 75: 1, 3, 5, 15, 25, 75 Factors of 147: 1, 3, 7, 21, 49, 147 When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 75 and 147 would be 3. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 22 and 87? What is the GCF of 149 and 102? What is the GCF of 94 and 1? What is the GCF of 105 and 150? What is the GCF of 15 and 85?