495 496 → Roman numeral CDXCV | Factorization 3× 5 × 11 Binary 1111011112 | |
Cardinal four hundred ninety-five Ordinal 495th(four hundred and ninety-fifth) | ||
495 is the integer after 494 and before 496. It is a pentatope number (and so a binomial coefficient
Contents
Kaprekar transformation
The Kaprekar's routine algorithm 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.
Example
For example, choose 589:
985 − 589 = 396963 − 369 = 594954 − 459 = 495The 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 = 099990 – 099 = 891 (rather than 99 - 99 = 0)981 – 189 = 792972 – 279 = 693963 – 369 = 594954 − 459 = 495The number 6174 has the same property for the four-digit numbers.