The Greatest Common Factor Of 28 And 35

Greatest Common Factor of 28 and 35 Calculatio from calculat.io

Introduction

As a professional teacher, one of the topics that I often encounter is finding the greatest common factor (GCF) of two numbers. In this article, we will focus on finding the GCF of 28 and 35. We will discuss what GCF is, how to find it, and the step-by-step solution to the problem.

What is GCF?

GCF, or the greatest common factor, is the greatest integer that divides two or more numbers without leaving any remainder. In simpler terms, it is the largest number that both numbers can be divided by without leaving any remainder. For example, the GCF of 12 and 18 is 6 because 6 is the largest number that can divide both 12 and 18.

How to Find GCF

There are different methods to find the GCF of two numbers. One way is to list down all the factors of each number and find the largest factor that they have in common. Another method is to use prime factorization. We will use the latter method to find the GCF of 28 and 35.

Step-by-Step Solution using Prime Factorization

1. Write the prime factorization of each number.

28 = 2 x 2 x 7
35 = 5 x 7

2. Identify the common prime factors. The common factor in this case is 7. 3. Multiply the common prime factors.

7 x 1 = 7

4. The GCF of 28 and 35 is 7.

Conclusion

In conclusion, finding the GCF of two numbers is a simple process once you understand the concept and the methods to solve it. In this article, we used prime factorization to find the GCF of 28 and 35, which is 7. By following the step-by-step solution, you can apply the same method to find the GCF of other numbers as well.