NCERT Class 6 Maths Playing with Numbers

Playing with Numbers

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

Please refer to attached file for NCERT Class 6 Maths Playing with Numbers