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  • Prof. S. Kannan

6174 - Mysterious Number?

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar.

This number is notable for the following rule:

  1. Take any four-digit number, using at least two different digits (leading zeros are allowed).

  2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.

  3. Subtract the smaller number from the bigger number.

  4. Go back to step 2 and repeat.

The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. [Read more]

D. R. Kaprekar

You may be interested to know that this interesting discovery was made by the Indian mathematician Dattatreya Ramachandra Kaprekar. He was born on January 17, 1905, in Dahanu, Maharashtra. Although he had no higher education in mathematics, he worked very hard in the field of "number theory" and did a lot of research on the calculation of various numbers. Kaprekar received his secondary education in Thane and studied at Fergusson University in Pune. In 1927 he won the Wrangler R. P. Paranjpe Mathematical Prize for an original work in mathematics.

He attended the University of Mumbai and received his bachelor's degree in 1929. Having never received any formal postgraduate education, he was a teacher at Nashik in Maharashtra, India, throughout his career (1930-1962). He published widely on topics such as recurring decimals, magic squares, and integers with special properties. He is also known as the "Ganitanad" of India.


Article by

Prof. Rahul Jadav,

Asst. prof / Dept. of EE.


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