495 (number)
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| 495 | |
|---|---|
| Cardinal | Four hundred ninety-five |
| Ordinal | Four hundred ninety-fifth |
| Factorization |  |
| Binary | 111101111 |
| Hexadecimal | 1EF |
495 is the integer after 494 and before 496. It is a pentatope number.
Contents |
[edit] Kaprekar transformation
The Kaprekar transformation is defined as follows for three-digit numbers:
- Start with a three-digit number with at least two digits different.
- Arrange the digits in ascending and then in descending order to get two three-digit numbers, adding leading zeros if necessary.
- Subtract the smaller number from the bigger number.
- 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.
[edit] Example
For example, choose 598:
- 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.
[edit] See also
- Collatz conjecture — sequence of unarranged-digit numbers always ends with the number 1.
[edit] References
- 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): 105–112. doi:.
