142857

From Conservapedia

Jump to: navigation, search

The number 142857 has the curious property that, if it is multiplied by any number from 1 to 6, the result is a number with the same digits in the same order (a cyclic permutation).

For example:

142857 × 1 = 142857
142857 × 2 = 285714
142857 × 3 = 428571
142857 × 4 = 571428
142857 × 5 = 714285
142857 × 6 = 857142


This property is closely related to the facts that

1/7 = 142857/999999

and that 1/7 expressed as a decimal is

0.142857142857142857142857142857...

Investigating the number 142857 can lead a student into an understanding of repeating decimals and rational numbers.


Similar Numbers

142857 is the only multi-digit decimal number with this property. However, if leading zeros are allowed on a number, some other examples are:

0588235294117647 (16 digits)
052631578947368421 (18 digits)
0434782608695652173913 (22 digits)
0344827586206896551724137931 (28 digits)
0212765957446808510638297872340425531914893617 (46 digits)

In octal (base-8 notation), the numbers 25 and 1463 have this property. There are no examples in hexadecimal (base-16).

Personal tools