The Greatest Common Factor Of 35 And 20

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Introduction

In mathematics, the greatest common factor (GCF) is the largest number that divides two or more numbers evenly. It is also known as the greatest common divisor (GCD). Finding the GCF of numbers is an important concept in arithmetic, algebra, and number theory. In this article, we will discuss how to find the GCF of 35 and 20.

Understanding Factors

To find the GCF of 35 and 20, we first need to understand what factors are. Factors are the numbers that can be multiplied to get a particular number. For example, the factors of 20 are 1, 2, 4, 5, 10, and 20. Similarly, the factors of 35 are 1, 5, 7, and 35.

Methods to Find GCF

There are several methods to find the GCF of two numbers, including prime factorization, division method, and Euclid's algorithm. In this article, we will discuss the division method to find the GCF of 35 and 20.

Division Method

The division method involves dividing the larger number by the smaller number and finding the remainder. Then, we divide the smaller number by the remainder and find the new remainder. We repeat this process until the remainder is zero. The last divisor is the GCF of the two numbers.

Step-by-Step Solution

Let's find the GCF of 35 and 20 using the division method. Step 1: Divide 35 by 20. We get a remainder of 15. Step 2: Divide 20 by 15. We get a remainder of 5. Step 3: Divide 15 by 5. We get a remainder of 0. Therefore, the GCF of 35 and 20 is 5.

Conclusion

In conclusion, the GCF of 35 and 20 is 5. We can find the GCF of two numbers using various methods, including prime factorization, division method, and Euclid's algorithm. The division method is a simple and effective way to find the GCF of two numbers. It is important to understand the concept of factors to find the GCF of numbers.