Number Magic

Number Theory Level 2

There exists a two digit number which yields the sum of its digits (of course, there is no remainder) when the original number is divided by the sum of its digits. Which is that two digit number?


The answer is 81.

Sumon Jose by Sumon Jose , 35, India

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5 solutions

Arijit Banerjee
Mar 9, 2014

this condition only will be satisfied by the perfect square numbers of two digits... so out of them only 81 satisfies the condition

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Zoom A Ray Mummah
Feb 21, 2014

The 2-digit number satisfies the condition that it is a perfect square since, Let x = Tens digit, y= units digit

If 10 x + y x + y = x + y \frac {10x + y}{x + y} = x + y

Then 10 x + y = ( x + y ) 2 10x + y = (x + y)^2

among the perfect squares, 16, 25, 36, 49, 64, and 81, only 81 satisfies the above condition.

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Saubia Ansari
Mar 25, 2014

81/9=9

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Shreyas Shastry
Mar 1, 2014

81=8+1

=81/9=9

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Muhammad Anwar
Feb 21, 2014

suppose the two number digit=x // sum of digits= y as per conditions x/y=y x=y2 putting the value of y from 1 through 9 it is only number 9 which satisfies the conditions of the question

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