Similarly, to multiply 142,857 by 5, simply do the same thing: the result is 714,285. No need to bother with long multiplication!
These two numbers are, in fact, parasitic numbers of orders 2 and 5 respectively: to multiply such a number of order n by n, simply perform a cyclic permutation of all its digits, moving the units digit to the front of the numeral. Parasitic numbers are known for every order from 2 to 9. There are infinitely many of each order. The two above are the smallest of their respective orders.
