The Six-Digit Number

Number Theory Level 3

Find a six-digit number whose product by 2, 3, 4, 5, or 6 contains the same digits as did the original number (in different order).


The answer is 142857.

Debjit Mandal by Debjit Mandal , 26, India

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3 solutions

Sack Net
Mar 9, 2014

its the value of (1/7). 1/7=0.142857 2/7=0.285714 ... 6/7=0.857142

2 Helpful 0 Interesting 0 Brilliant 0 Confused

i did it in the same way

akash deep - 7 years, 1 month ago
Rajen Kapur
Mar 16, 2014

All powers of 10, i.e. decimal system are co-prime with 7 hence this cyclic behavior is being manifested.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sharky Kesa
Mar 8, 2014

This is known as a cyclic number. Click here to find out more about them.

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