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Undo revision 606475 by JillH (Talk)
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).
[[Category:Mathematics]]