Magical numbers :Cyclic numbers

The cyclic numbers are the numbers which when multiplied with any other number yields the same number but in some other form.

The first cyclic number is 142857, which can be easily remembered as the final output of 1/7.

1/7 = 0.142857142857...

So as we can see 142857 is repeated in the division 1/7, and can be easily remembered by this method.


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

Now as we can easily see the number is just in the cyclic form in all the multiplications.

For multiplication of the integers above 7, we follow the procedure given below:

142857 × 8 = 1142856
1 + 142856 = 142857

142857 × 815 = 116428455
116 + 428455 = 428571

So as you can see this number is very magical!!!

Similar numbers can be found:
0588235294117647 (16 digits)
052631578947368421 (18 digits)
0434782608695652173913 (22 digits)
0344827586206896551724137931 (28 digits)
0212765957446808510638297872340425531914893617 (46 digits)
0169491525423728813559322033898305084745762711864406779661 (58 digits)
016393442622950819672131147540983606557377049180327868852459 (60 digits)

Keep following the blog for more such amazing numbers and more!!!

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