495 (number)

Last updated
494 495 496
Cardinal four hundred ninety-five
Ordinal 495th
(four hundred ninety-fifth)
Factorization 32 × 5 × 11
Greek numeral ΥϞΕ´
Roman numeral CDXCV
Binary 1111011112
Ternary 2001003
Senary 21436
Octal 7578
Duodecimal 35312
Hexadecimal 1EF16

495 (four hundred [and] ninety-five) is the natural number following 494 and preceding 496. It is a pentatope number [1] (and so a binomial coefficient ). The maximal number of pieces that can be obtained by cutting an annulus with 30 cuts. [2]

Contents

Kaprekar transformation

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

  1. Take any three-digit number, other than repdigits 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.

Example

For example, choose 495:

495

The only three-digit numbers for which this function does not work are repdigits such as 111, which give the answer 0 after a single iteration. All other three-digit numbers work if leading zeros are used to keep the number of digits at 3:

211 – 112 = 099
990 – 099 = 891 (rather than 99 – 99 = 0)
981 – 189 = 792
972 – 279 = 693
963 – 369 = 594
954 − 459 = 495

The number 6174 has the same property for the four-digit numbers, albeit has a much greater percentage of workable numbers.

See also

Related Research Articles

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One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione, from mille, "thousand", plus the augmentative suffix -one.

<span class="mw-page-title-main">1,000,000,000</span> Natural number

1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001. With a number, "billion" can be abbreviated as b, bil or bn.

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In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.

10,000,000 is the natural number following 9,999,999 and preceding 10,000,001.

100,000,000 is the natural number following 99,999,999 and preceding 100,000,001.

363 is the natural number following 362 and preceding 364.

20,000 is the natural number that comes after 19,999 and before 20,001.

30,000 is the natural number that comes after 29,999 and before 30,001.

70,000 is the natural number that comes after 69,999 and before 70,001. It is a round number.

80,000 is the natural number after 79,999 and before 80,001.

90,000 is the natural number following 89,999 and preceding 90,001. It is the sum of the cubes of the first 24 positive integers, and is the square of 300.

888 is the natural number following 887 and preceding 889.

9000 is the natural number following 8999 and preceding 9001.

99 (ninety-nine) is the natural number following 98 and preceding 100.

The number 6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule:

  1. Take any four-digit number, using at least two different digits.
  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.

References

  1. "Sloane's A000332". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-16.
  2. Sloane, N. J. A. (ed.). "SequenceA000096". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.