Multiply 142857 by two and you get 285714: the same six digits, started from a different place. Times three is 428571, times four 571428, times five 714285, times six 857142, the same ring of digits turning each time like the dial of a combination lock. The number is what you get when you write out one seventh, 0.142857142857…, and that is where the trick comes from. So multiply it by seven, the number it was cut from, and the ring breaks: 999999, as close as six digits can come to being whole again.