Question

list the first ten multiples of 9, then keeping in mind the 'sum' of the digits' for divisibility by 3, devise a rule for divisibility by 9

Answer 1

The first 10 multiples of 9 :

9, 18, 27, 36, 45, 54, 63, 72, 81 and 90

Rule for Divisibility of 9

⇒ Rule for Divisibility of 9 follows closely to the Rule for Divisibility of 3

⇒ Rule for Divisibility of 3= If the sum of all the digits in the number is divisible by 3, the number is divisible by 3.

⇒ Rule for Divisibility of 9 = If the sum of all the digits in the number is divisible by 9, the number is divisible by 9.

Example 1: 18

sum of the digits in 18 = 1 + 8 = 9

Check divisibility ⇒ 9 is divisible by 9, therefore 18 is divisible by 9

Example 2: 4887

sum of the digits in 4887 = 4 + 8 + 8 + 7  = 27, therefore 4887 is divisible by 9

Answer 2

Answer:

9 , 18 , 27 , 36 , 45 , 63 , 54 , 72 , 81 and 90 are the required numbers.