Question

Consider the numbers of the form 6, where n is a natural number. Check whether there is any
value of n for which 6n is divisible by 9.

Answer 1

We should get the multiples of 9 that are divisible by both divisible by 9 and 6.

The multiples of 9 that are divisible by both 6 and 9 are the multiples of nine where 9 is multiplied by even numbers.

Examples :

2 × 9 = 18

4 × 9 = 36

6 × 9 = 54

8 × 9 = 72

All these are divisible by both 6 and 9.

So we get the values of n by :

6 n / 9 = 2

6n = 18

n = 3

6n / 9 = 4

6n = 36

n = 6

6n / 9 = 6

n = 9


6n / 9 = 8

6n = 72

n = 12

From this we get a pattern for the value of n which is :

The next value of n from n is n +3

The values of n are thus :

3, 6, 9, 12....... ,n + 3