Calculations
| List of numbers 100000 142857 1000000 |
|
|---|---|
| Cardinal | One hundred forty-two thousand, eight hundred fifty-seven |
| Ordinal | 142,857th |
| Roman numeral | CXLMMDCCCLVII |
| Factorization | 142857 = 33 • 11 • 13 • 37 |
| Binary | 100010111000001001 |
| Hexadecimal | 22E09 |
| Octal | 427011 |
- 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 multiply by an integer greater than 7, there is a simple process to get to a cyclic permutation of 142857. By adding the first six digits (ones through hundred thousands) to the remaining digits and repeating this process until you have only the six digits left, it will result in a cyclic permutation of 142857
- 142857 × 8 = 1142856
- 1 + 142856 = 142857
- 142857 × 815 = 116428455
- 116 + 428455 = 428571
- 1428572 = 142857 × 142857 = 20408122449
- 20408 + 122449 = 142857
Multiplying by a multiple of 7 will result in 999999 through this process
- 142857 × 74 = 342999657
- 342 + 999657 = 999999
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.
- 8572 = 734449
- 1422 = 20164
- 734449 − 20164 = 714285
It is the repeating part in the decimal expansion of the rational number 1/7 = 0.142857. Thus, multiples of 1/7 are simply repeated copies of the corresponding multiples of 142857:
- 1 ÷ 7 = 0.142857
- 2 ÷ 7 = 0.285714
- 3 ÷ 7 = 0.428571
- 4 ÷ 7 = 0.571428
- 5 ÷ 7 = 0.714285
- 6 ÷ 7 = 0.857142
- 7 ÷ 7 = 0.999999
- 8 ÷ 7 = 1.142857
- 9 ÷ 7 = 1.285714
- …
In base 10, 142,857 is a Harshad number and a Kaprekar number.
Read more about this topic: 142857 (number)
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