D.R.Kaprekar: Indian Mathematician

The readers may recall that I talked about Ramanujan sometime back. Today I introduce to my readers, a much less known Indian Mathematician.

Dattaraya Ramchandra Kaprekar, born 1905 worked on the number theory. He had no formal postgraduate training and worked as a schoolteacher in Nasik, India.

His claim to fame is the Kaprekar constant 6174. Start with any four digit number, with no repeating digits – say Z. Let A and B be two numbers formed by rearranging the digits of Z, such that A is the highest number that is possible, and B the smallest. Subtract B from A. If this is not 6174, continue the same way now taking this number to be Z. For example, starting with Ramanujan number 1729:

9721-1279 = 8442
8442-2448 = 5994
9954-4599 = 5355
5553-3555 = 1998
9981-1899 = 8082
8820-0288 = 8532
8532-2358 = 6174
7641-1467 = 6174

He also gave the world Harshad numbers: numbers that can be divided by the sum of their digits – for example 12, which is divisible by 3.