chapter  16
11 Pages

Cyclic Numbers and their Secret

WithMalcolm E Lines

The number 142,857 has long been recognized by those interested in number oddities as one of the most remarkable of integers. When multiplied by any number from 1 to 6 the result always consists of the same digits and, more remarkably still, these digits always appear in the same cyclic order, but with each number commencing at a different point. Thus we find 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