Q:

What is the GCF of 40 and 144?

Accepted Solution

A:
Solution: The GCF of 40 and 144 is 8 Methods How to find the GCF of 40 and 144 using Prime Factorization One way to find the GCF of 40 and 144 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 40? What are the Factors of 144? Here is the prime factorization of 40: 2 3 × 5 1 2^3 × 5^1 2 3 × 5 1 And this is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 3 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 40 and 144 by multiplying all the matching prime factors to get a GCF of 40 and 144 as 4: Thus, the GCF of 40 and 144 is: 4 How to Find the GCF of 40 and 144 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 40 and 144 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, 40 and 144: Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8. Since 8 is the largest of these common factors, the GCF of 40 and 144 would be 8. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 65 and 63? What is the GCF of 16 and 43? What is the GCF of 132 and 70? What is the GCF of 133 and 89? What is the GCF of 19 and 115?