142857 (number)
From Wikipedia, the free encyclopedia
142,857 is the best-known cyclic number. If you multiply the number by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself.
| List of numbers 100000 142857 1000000 |
|
|---|---|
| Cardinal | One hundred and forty-two thousand, eight hundred and fifty-seven |
| Ordinal | 142,857th |
| Factorization |  |
| Binary | 100010111000001001 |
| Hexadecimal | 22E09 |
- 1 × 142,857 = 142,857
- 2 × 142,857 = 285,714
- 3 × 142,857 = 428,571
- 4 × 142,857 = 571,428
- 5 × 142,857 = 714,285
- 6 × 142,857 = 857,142
- 7 × 142,857 = 999,999
If you continue multiplying it by larger numbers, the result will always be some sort of variation on 142,857 or 999,999. For example:
- 8 × 142,857 = 1,142,856 (Add the first digit to the last, and the last six will be 142,857.)
- 42 × 142,857 = 5,999,994 (Add the first digit to the last, and the last six will be 999,999.)
- 142,857 × 142,857 = 20,408,122,449 (Add the first five digits to the last six, and the last six will be 142,857.)
If you divide it by 2 or by 5, you are doing 142857×5/10 or 142857×2/10 respectively, so you get the corresponding cyclic permutations with a decimal point:
- 142,857 ÷ 2 = 71,428.5
- 142,857 ÷ 5 = 28,571.4
If you square the last three digits and subtract the square of the first three digits, you also get back a cyclic permutation of the number.
In base 10, 142,857 is a Harshad number and a Kaprekar number.
It is the repeating part in the decimal expansion of the rational number 1/7 = 0 . 142857 142857 14… Thus, multiples of 1/7 are simply repeated copies of the corresponding multiples of 142857:
- 1/7 = 0 . 142857 142857 142857 14…
- 2/7 = 0 . 285714 285714 285714 28…
- 3/7 = 0 . 428571 428571 428571 42…
- 4/7 = 0 . 571428 571428 571428 57…
- 5/7 = 0 . 714285 714285 714285 71…
- 6/7 = 0 . 857142 857142 857142 85…
