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Question

The sum of the digits of a 3 digit number is subtracted from the number.

The resulting number is always _____


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Solution

Explanation

Divisibility rule: Divisibility means that a number goes evenly with no remainder into a number.

For example, 4 goes evenly into 32. So, 32 is divisible by 2.

Let the 3 digit number be: XYZ.

As per the question, we have to find the divisibility of number P (let),

P=(100X+10Y+Z)-(X+Y+Z)

P=(99X+9Y)

P=9(11X+Y)

Which is divisible by 9.

Hence, if the sum of three digit number is subtracted from the number.

The resulting number is always divisible by 9.


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