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Kaprekar Number

D. R. Kaprekar (Dattatreya Ramchandra Kaprekar) introduced an amazing concept Kaprekar number in number theory.

Kaprekar number is a natural number whose square when divided into two equal or non-equal parts; left and right, then the sum of both parts must be equal to the original number. None of the parts should have the value zero.

The Procedure

Step 1: Consider a natural number n.

Step 2: Square the number n2.

Step 3: Divide the value after square into two equal or non-equal parts: left x or x-1 digits and right y digits.

Step 4: Add both left and right parts: (x + y) or (x-1 + y).

Step 5: If the resultant z is equal to the original number n, then number n is a Kaprekar number, else not.

For Example

Number n: 9

Square the number n2: 92 => 81.

Divide the value after square into two equal or non-equal parts: 8 and 1.

Add both left and right parts: 8 + 1=> 9.

Here the resultant 9 is equal to the original number n. Hence, 9 is a Kaprekar number.

Number n: 45

Square the number n2: 452 => 2025.

Divide the value after square into two equal or non-equal parts: 20 and 25.

Add both left and right parts: 20 + 25=> 45.

Here the resultant 45 is equal to the original number n. Hence, 45 is a Kaprekar number.

Number n: 55

Square the number n2: 552 => 3025.

Divide the value after square into two equal or non-equal parts: 30 and 25.

Add both left and right parts: 30 + 25=> 55.

Here the resultant 55 is equal to the original number n. Hence, 55 is a Kaprekar number.

Number n: 99

Square the number n2: 992 => 9801.

Divide the value after square into two equal or non-equal parts: 98 and 01.

Add both left and right parts: 98 + 01=> 99.

Here the resultant 99 is equal to the original number n. Hence, 99 is a Kaprekar number.

Number n: 297

Square the number n2: 2972 => 88209.

Divide the value after square into two equal or non-equal parts: 88 and 209.

Add both left and right parts: 88 + 209 => 297.

Here the resultant 297 is equal to the original number n. Hence, 297 is a Kaprekar number.

Hope you have understood this amazing concept of Kaprekar number. In case of any issue, kindly provide your valuable comments.

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