Kaprekar''s Constant

What is Kaprekar's Constant?

Discovered by Indian mathematician D. R. Kaprekar in 1949, 6174 is a remarkable number. Take any 4-digit number with at least two distinct digits, sort its digits in descending and ascending order, subtract the smaller from the larger - and repeat. You'll always land on 6174.

Try it yourself

Kaprekar's Constant

Any 4-digit number with 2+ distinct digits reaches 6174 in at most 7 steps.

How it works: Sort digits descending - ascending, subtract. Repeat until 6174.

Why does this work?

Once you reach 6174, the process loops: 7641 - 1467 = 6174. It's a fixed point of the Kaprekar routine. Mathematicians have verified that every valid 4-digit number converges here in at most 7 iterations - no exceptions.