- 6174 (number)
Number|number= 6174
range = 1000 - 10000
cardinal = Six thousand one hundred seventy-four
ordinal = th
factorization =
roman = VⅯCLXXIV
bin = 1100000011110
oct = 14036
duo =
hex = 181E6174 is known as Kaprekar's constant or Kaprekar's operation [ [http://plus.maths.org/issue38/features/nishiyama/index.html Mysterious number 6174] ] cite journal|author=Kaprekar DR|title=An Interesting Property of the Number 6174 | journal=
Scripta Mathematica |volume=15|pages=244–245|year=1955] cite journal|author=Kaprekar DR|title=On Kaprekar Numbers | journal=Journal of Recreational Mathematics|volume=13|issue=2|pages=81–82|year=1980] after theIndia nmathematician D. R. Kaprekar . This number is notable for the following property:#Take any four-digit number with at least two digits different. (Leading zeros are allowed.)
#Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
#Subtract the smaller number from the bigger number.
#Go back to step 2.The above operation will always reach 6174 in at most 7 steps and it stops there. Once 6174 is reached, the process will keep yielding 7641 – 1467 = 6174. For example, choose 5342:
:5432 – 2345 = 3087:8730 – 0378 = 8352:8532 – 2358 = 6174
The only four-digit numbers for which this function does not work are
repdigit s such as 1111, which give the answer 0 after a single iteration. All other four-digits numbers work if leading zeros are used to keep the number of digits at 4::2111 – 1112 = 0999:9990 – 0999 = 8991 (rather than 999 - 999 = 0):9981 – 1899 = 8082:8820 – 0288 = 8532:8532 – 2358 = 6174
495 also has the same property for three-digit numbers.
ee also
*
Collatz conjecture External links
* [http://plus.maths.org/issue38/features/nishiyama/index.html Mysterious Number 6174 Article]
* [http://mathpoint.blogspot.com/2006/12/mysterious-6174-revisited.html The mysterious 6174 revisited]
* [http://kaprekar.sourceforge.net/ Kaprekar Series Generator]References
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