3.1 Introduction

Ramesh has 6 marbles with him. He wants to arrange them in rows in such a way that each row has the same number of marbles. He arranges them in the following ways and matches the total number of marbles.

(i) 1 marble in each row Number of rows = 6
Total number of marbles = 1 × 6 = 6

(ii) 2 marbles in each row Number of rows = 3
Total number of marbles = 2 × 3 = 6

(iii) 3 marbles in each row Number of rows = 2
Total number of marbles = 3 × 2 = 6

(iv) He could not think of any arrangement in which each row had 4 marbles or
5 marbles. So, the only possible arrangement left was with all the 6 marbles in a row.
Number of rows = 1
Total number of marbles = 6 × 1 = 6
From these calculations Ramesh observes that 6 can be written as a product
of two numbers in different ways as
6 = 1 × 6;
6 = 2 × 3;
6 = 3 × 2;
6 = 6 × 1

From 6 = 2 × 3 it can be said that 2 and 3 exactly divide 6. So, 2 and 3 are exact divisors of 6. From the other product 6 = 1 × 6, the exact divisors of 6 are found to be 1 and 6.

Thus, 1, 2, 3 and 6 are exact divisors of 6. They are called the factors of 6.
Try arranging 18 marbles in rows and find the factors of 18.