142857: The Cyclic Number That Pulled Me In

This number will probably pull you in too!

The cyclic number — Illustrative art created by the author

A while back, I wrote an essay on the curious case of the interesting number paradox. While concluding this essay, I requested readers to share their favourite number(s). I got a few interesting entries in the comments section. Out of the whole lot, Fabiano Fagundes’s comment took the cake for me:

“Mine is 142857. No kidding. I love the only cyclic number in the decimal system.”

Until this point, I did not know about this number. So, naturally, I had to investigate. The deeper I dove in, the more interesting this number got. So, here we are.

I will start by sharing some of the interesting properties of this number. Following this, I will explain why this number is a cyclic number. Finally, I will touch upon the generalised notion of cyclic numbers. If you are interested in this sort of stuff, strap in, and let us begin.

The Mathematical Carousel

Let us start with the number in question: 142857

To begin, let me just arrange the digits that constitute this number in their ascending order as follows (note that we have 6 digits in total):

1, 2, 4, 5, 7, 8