495 (number)

← 494 495 496 →
List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	four hundred ninety-five
Ordinal	495th (four hundred and ninety-fifth)
Factorization	3^2× 5 × 11
Roman numeral	CDXCV
Binary	1111011112
Ternary	2001003
Quaternary	132334
Quinary	34405
Senary	21436
Octal	7578
Duodecimal	35312
Hexadecimal	1EF16
Vigesimal	14F20
Base 36	DR36

495 is the integer after 494 and before 496. It is a pentatope number^[1] (and so a binomial coefficient ${\displaystyle {\tbinom {12}{4}}}$).

Kaprekar transformation

The Kaprekar transformation is defined as follows for three-digit numbers:

1. Start with a three-digit number with at least two digits different.
2. Arrange the digits in ascending and then in descending 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.

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 589:

985 − 589 = 396

963 − 369 = 594

954 − 459 = 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-digits 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.

See also

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

References

1. "Sloane's A000332". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-16.

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