A Short Note on Kaprekar's Constant 6174

Abstract

Kaprekar's constant 6174 is one of the most celebrated numbers in recreational mathematics. Starting with any four-digit number having at least two distinct digits, a simple procedure involving the rearrangement of digits and subtraction eventually produces the number 6174. Once reached, the value remains unchanged under further applications of Kaprekar's operation. In this note, we introduce Kaprekar's procedure, present several illustrative examples, establish the fixed-point property of 6174, prove a basic divisibility property of the procedure, and discuss the convergence phenomenon that makes 6174 so remarkable. The topic provides an attractive example of how elementary arithmetic can lead to unexpected and fascinating numerical phenomena.