The Gcf Of 10 And 25: Explanation And Solution

GCF of 10 and 25 How to Find GCF of 10, 25? from www.cuemath.com

Introduction

When you are studying mathematics, you will come across different concepts and problems that require you to find their solutions. One of these concepts is the greatest common factor (GCF). The GCF is the largest number that divides two or more integers without leaving a remainder. In this article, we will discuss the GCF of 10 and 25 and provide you with an explanation and solution.

Understanding the Problem

Before we dive into finding the GCF of 10 and 25, we need to understand what these numbers mean. 10 and 25 are both integers, which means they are whole numbers. 10 is a multiple of 5 and 2, while 25 is a multiple of 5 and 5. In other words, 10 = 5 x 2 and 25 = 5 x 5.

Finding the Factors

To find the GCF of 10 and 25, we need to determine their factors. Factors are the numbers that can be multiplied together to get the original number. For example, the factors of 10 are 1, 2, 5, and 10. The factors of 25 are 1, 5, and 25.

Identifying Common Factors

Once we have found the factors of both 10 and 25, we need to identify their common factors. Common factors are the numbers that both 10 and 25 share. In this case, the common factor between 10 and 25 is 5.

Finding the Greatest Common Factor

Now that we have identified the common factor, we need to find the greatest common factor. The greatest common factor is the largest number that both 10 and 25 can be divided by without leaving a remainder. In this case, the greatest common factor of 10 and 25 is 5.

Verification

To verify that 5 is indeed the greatest common factor of 10 and 25, we can divide both numbers by 5. 10 ÷ 5 = 2 and 25 ÷ 5 = 5. Both of these divisions result in whole numbers, which means that 5 is a factor of both 10 and 25.

Conclusion

In conclusion, the GCF of 10 and 25 is 5. This means that 5 is the largest number that both 10 and 25 can be divided by without leaving a remainder. Finding the GCF requires us to first find the factors of each number, then identify their common factors, and finally find the greatest common factor. This is an important concept in mathematics that will help you solve various problems in the future.

Practice Problem

Find the GCF of 16 and 24.

Solution

The factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The common factors of 16 and 24 are 1, 2, 4, and 8. The greatest common factor of 16 and 24 is 8.