Q:

What is the GCF of 21 and 147?

Accepted Solution

A:
Solution: The GCF of 21 and 147 is 21 Methods How to find the GCF of 21 and 147 using Prime Factorization One way to find the GCF of 21 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 21? What are the Factors of 147? Here is the prime factorization of 21: 3 1 × 7 1 3^1 × 7^1 3 1 × 7 1 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 21 and 147 by multiplying all the matching prime factors to get a GCF of 21 and 147 as 441: Thus, the GCF of 21 and 147 is: 441 How to Find the GCF of 21 and 147 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 21 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, 21 and 147: Factors of 21: 1, 3, 7, 21 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, 7, 21. Since 21 is the largest of these common factors, the GCF of 21 and 147 would be 21. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 110 and 81? What is the GCF of 24 and 3? What is the GCF of 10 and 131? What is the GCF of 33 and 101? What is the GCF of 104 and 90?