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.

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.

$857^2\; =\; 734449\backslash ,$

$142^2\; =\; 20164\backslash ,$

$734449\; -\; 20164\; =\; 714285\backslash ,$

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…

Integers

142857 (nombre) | Cento e quarenta e dois mil oitocentos e cinquenta e sete | 142857 (tal)