Question

write the converse of the following(iv) If the sum of the digits of a number is divisible by 3 then the number is divisible
by 3.
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Answer 1

Answer:

For the given statement, If the sum of the digits of a number is divisible by 3 then the number is divisible by 3.

The converse of the statement is "If a number can be divided by 3, then the sum of the digits of that number is also divisible by 3."

eg. 156 is divisible by 3.

Digital sum is 1+5+6=12

12 is also divisible by 3.  

156=100+50+6

      =(1+5+6)+(99+45)

      =(1+5+6)+3(33+15)

156 and 3(33+15) both are divisible by 3.

So, digital sum 1+5+6=12 is also divisible by 3.

So,it is possible for checking divisibility of numbers having more digits by 3