Question

The sum of a number is subtracted from the number, the resulting number is always divisible by

Answer 1

Answer:

Step-by-step explan

Let the number be xy , that is 10x+y .

Given, Sum of digits = x + y.

Question : The sum of digits of a number is subtracted from a number, the resulting number is always divisible by.

Number - Sum of digits

= ( 10 x + y) - ( x + y)

= 10x + y - x - y

= 10x - x + \cancel{ y }- \cancel{y}

= 9x .

So , 9x has factors 9 & x. Therefore, 9x is always divisible by 9 .

The sum of the digits of a number is subtracted from a number , the resulting number is always divisible by 9 .

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