7×142857

7×142857 equals 999,999. The number 142,857 is notable in number theory as a six-digit cyclic number, arising as the repeating block of the decimal expansion of 1/7: 0.142857142857... This block has the property that multiplying by integers 2 through 6 yields cyclic permutations of the same six digits: 2×142857 = 285714, 3×142857 = 428571, 4×142857 = 571428, 5×142857 = 714285, 6×142857 = 857142. In all cases the digits are rotations of 142857. When multiplied by 7, the result is 999,999, i.e., 10^6 − 1.

This relation is tied to the fact that 7 divides 10^6 − 1 and that the decimal expansion of 1/7 has a six-digit repeating period. Consequently, 142,857 is a classic example of a cyclic number in base 10. The phenomenon is closely related to properties of full reptend primes and to the concept of repetends in recurring decimals. The number is often cited in recreational mathematics for its symmetry and as a demonstration of how multiplication can correspond to digit rotation.