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 ninety-fifth)
Factorization	32 × 5 × 11
Divisors	1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495
Greek numeral	ΥϞΕ´
Roman numeral	CDXCV, 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.

Mathematics

• It is a composite number, with the divisors being 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495.
• It is a generalized pentagonal number.

Kaprekar's routine

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.

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

See also

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

References

Sources

• 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.