Question

If the sum of the digitsof any integer between 100 and 1000 is subtracted from the same integer the resulting number is always divisible by​

Answer 1

Answer:

The result is always divisible by 9.

Of course the result is also divisible by 3 or 1.

For example, consider the number 236. Sum of the digits is 2+3+6=11. Now after subtracting the sum of the digits (11), from the original number 236, we get, 236–11 = 225.

225 is divisible by 1,3 & 9.

In general for any 3 digit number having digits a,b & c at 100’s, 10’s & units place resp., the number is 100a+ 10b + c. After subtracting sum

of the digits (a+b+c), from the original number (100a+10b+c), we get, 99a+9b = 9(11a+b), thus result is divisible by 9. And since 9 is divisible by 3 & 1, result is also divisible by 3 & 1.