Question

Sum of digits of a three digit number of subtracted from the number theb resulting number is divisible by

Answer 1

Step-by-step explanation:

Let, any random three digit number say 568, its digits sum is 19. Now, on subtracting 19 from 568, we get 549 which is divisible by 9. Hence, the resultant number after subtracting sum of three digits form the the number will always be divisible by 9.Answer:  The resulting number is divisible by 9.

Step-by-step explanation:  Given that the sum of the digits of a 3 digit number is subtracted from the number.

We are to find the number by which the resulting number is divisible.

Let x, y and z be the digits in the hundred's place, ten's place and one's place of the given 3 digit number.

Then, the number is written as follows :

n = 100 x+ 10 y + z.

And, the sum of the digits of the number n is (x + y + z).

Therefore, we have

\begin{lgathered}n-(x+y+z)\\\\=(100x+10y+z)-x-y-z\\\\=100x+10y+z-x-y-z\\\\=99x+9y\\\\=9(11x+y).\end{lgathered}n−(x+y+z)=(100x+10y+z)−x−y−z=100x+10y+z−x−y−z=99x+9y=9(11x+y).

That is, the factors of the given number are 9 and (11 x + y). Since x and y are unknowns, so the only confirmed number which divides the resulting number is 9.

Thus, the resulting number is divisible by 9.