Gcf Of 40 And 72: Explanation And Solution

GCF of 40 and 72 How to Find GCF of 40, 72? from en.asriportal.com

Introduction

Are you struggling with finding the greatest common factor (GCF) of 40 and 72? Do not worry, as this article will provide you with a detailed explanation and solution to this problem.

Definition of GCF

Before we proceed, let us first define what GCF means. The greatest common factor is the largest number that can divide two or more integers without leaving a remainder.

Finding the Prime Factors of 40 and 72

To determine the GCF of 40 and 72, we first need to find their prime factors. We can do this by dividing each number by its smallest prime factor until we are left with only prime numbers. For 40, its smallest prime factor is 2. We can divide 40 by 2 to get 20, then divide 20 by 2 to get 10, and divide 10 by 2 to get 5. Thus, the prime factorization of 40 is 2 x 2 x 2 x 5, which we can write as 2^3 x 5. For 72, its smallest prime factor is also 2. We can divide 72 by 2 to get 36, then divide 36 by 2 to get 18, then divide 18 by 2 to get 9. However, 9 is not divisible by 2, so we need to divide it by its smallest prime factor, which is 3. We get 3 x 3 = 9. Thus, the prime factorization of 72 is 2 x 2 x 2 x 3 x 3, which we can write as 2^3 x 3^2.

Identifying the Common Factors

Now that we have the prime factorizations of 40 and 72, we can identify their common factors by multiplying the primes that they share. In this case, the common factors of 40 and 72 are 2^3, which is 8, since both numbers have three 2's in their prime factorizations. Note that we do not consider the other prime factors, namely 5 and 3^2, because they are not present in both numbers.

Determining the GCF

Since 8 is the largest common factor of 40 and 72, it is also their GCF. Therefore, the GCF of 40 and 72 is 8.

Checking the Answer

We can verify our answer by dividing 40 and 72 by 8 and checking if the result is a whole number. 40 divided by 8 is 5, which is a whole number. 72 divided by 8 is 9, which is also a whole number. Therefore, our answer is correct.

Conclusion

In summary, finding the GCF of 40 and 72 involves identifying their prime factors, determining their common factors, and selecting the largest common factor as the GCF. The GCF of 40 and 72 is 8, which we can verify by dividing the numbers by 8 and checking if the result is a whole number.