Question

Sum of the digits of a 3 digit number is subtracted from.the number .the resulting number is divisible by

Answer 1

3 is the answer to this question

Answer 2

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

$n-(x+y+z)\\\\=(100x+10y+z)-x-y-z\\\\=100x+10y+z-x-y-z\\\\=99x+9y\\\\=9(11x+y).$

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.