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495 (number)

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Natural number
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Natural number
← 494495 496 →
Cardinalfour hundred ninety-five
Ordinal495th
(four hundred ninety-fifth)
Factorization32 × 5 × 11
Greek numeralΥϞΕ´
Roman numeralCDXCV,cdxcv
Binary1111011112
Ternary2001003
Senary21436
Octal7578
Duodecimal35312
Hexadecimal1EF16

495 (four hundred [and] ninety-five) is thenatural number following494 and preceding496.

Mathematics

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TheKaprekar's routine algorithm is defined as follows for three-digit numbers:

  1. Take any three-digit number, other thanrepdigits such as 111. Leading zeros are allowed.
  2. Arrange the digits in descending and then in ascending order to get two three-digit numbers, adding leading zeros if necessary.
  3. Subtract the smaller number from the bigger number.
  4. Go back to step 2 and repeat.

Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495.

The number6174 has the same property for the four-digit numbers, albeit has a much greater percentage of workable numbers.[1]

See also

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  • Collatz conjecture — sequence of unarranged-digit numbers always ends with the number 1.

References

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  1. ^Hanover 2017, p. 14, Operations.
  • Eldridge, Klaus E.; Sagong, Seok (February 1988). "The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit Numbers".The American Mathematical Monthly.95 (2). The American Mathematical Monthly, Vol. 95, No. 2:105–112.doi:10.2307/2323062.JSTOR 2323062.
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