Gcf For 10 And 25: Explanation And Solution

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

Introduction

In math, GCF stands for Greatest Common Factor. It is the largest number that divides two or more numbers without leaving a remainder. For example, the GCF of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 without leaving a remainder. In this article, we will be discussing the GCF for 10 and 25.

Explanation

To find the GCF for 10 and 25, we need to find the factors of each number. A factor is a number that divides another number without leaving a remainder. The factors of 10 are 1, 2, 5, and 10. The factors of 25 are 1, 5, and 25. The common factors of 10 and 25 are 1 and 5. However, we are looking for the greatest common factor, which is 5.

Step-by-Step Solution

1. Write down the factors of 10: 1, 2, 5, 10. 2. Write down the factors of 25: 1, 5, 25. 3. Identify the common factors of 10 and 25: 1, 5. 4. Choose the largest common factor, which is 5. 5. Therefore, the GCF of 10 and 25 is 5.

Alternative Solution

Another way to find the GCF of 10 and 25 is to use prime factorization. Prime factorization is the process of breaking down a number into its prime factors, which are the smallest prime numbers that can multiply to make the number. The prime factors of 10 are 2 and 5. The prime factors of 25 are 5 and 5. The common prime factor is 5. Therefore, the GCF of 10 and 25 is 5.

Real-World Example

The concept of GCF is used in many real-world situations. For example, if you are a baker and you want to make as many cakes as possible using a certain number of eggs and flour, you would need to find the GCF of the number of eggs and the amount of flour required for each cake. This will give you the maximum number of cakes you can make with the available ingredients.

Conclusion

In conclusion, the GCF for 10 and 25 is 5. This can be found by either listing the factors or using prime factorization. GCF is a useful concept in many real-world situations, and it is important to understand how to find it.