495 (number)

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 ${\displaystyle {\tbinom {12}{4}}}$).

← 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 ninety-fifth)
Factorization	3^2 × 5 × 11
Greek numeral	ΥϞΕ´
Roman numeral	CDXCV
Binary	1111011112
Ternary	2001003
Octal	7578
Duodecimal	35312
Hexadecimal	1EF16

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-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.