142,857: A Truly Magical Number

One hundred and forty-two thousand eight hundred and fifty-seven seems like any number, but it is not. You can multiply it by 2, now by 3 and then by 4… You’ll always be surprised.

142857 magical number

142857 x 3 = 428571 (we get a number with the same digits, with 1 sandwiched at the end).

142857 x 2 = 285714 (again we get the same digits, now with 1 and 4 interspersed at the end).

142857 x 6 = 857142 (1, 4 and 2 were walked at the end).

142857 x 4 = 571428 (the result shows us that the 1, 4, 2 and 8 jumped to the end of the queue).

142857 x 5 = 714285 (again, a product with the same digits: 1, 4, 2, 8, and 5 left at the end.

In various books of mathematical curiosities, the mysterious 142,847 is discussed. In 1943, in one of his books on mathematical curiosities, Malba Tahan (pseudonym of Professor Julio César de Mello e Souza) pointed out the behavior of this number when multiplied by 7 and 8:

142857 x 7 = 999999

142857 x 8 = 1142856 (we have the same digits, except for 7, which has become the initial 1 and the final 6).

Speaking of the number 7, do you know what the result of dividing 1 by 7 is? 0.14285714285714…

That’s why, even if you’re not a numbers maniac, it’s impossible not to show some interest in 142,857.