# Cyclic Number

There is a very interesting concept called Cyclic Number.

Cyclic Numbers can be defined as a number with n digits, which, when multiplied by 1, 2, 3, …, n produces the same digits in a different order.

There are few very famous cyclic numbers. We have given a puzzle question below, if you could answer the puzzle your concept of cyclic number will be crystal clear. That’s the reason we have not given example for cyclic numbers.

Can you find a number which added to itself one or several times will give a total having the same digits as that number but differently and after the sixth addition will give a total of all nines?

#### Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

## 17 thoughts to “Cyclic Number”

1. Sounak says:

I think the number is 142857.
Because, 142857 x 7 = 999999
And the number given is cyclic.
Even, 588235294117647 and
52631578947368421 is also a cyclic number because.
588235294117647 x 17 = 9999999999999999
52631578947368421 x 19 = 999999999999999999
And the numbers which is multiplied below 17 (5882…7647) and 19 (5263…8421) is 100 % cyclic.

2. Harmesh says:

No clue. Please make me understand the concept of cyclic number with illustration

3. kartik maurya says:

the next number is 0588235294117647 which on the 16th multiplication will give 9999999999999999

4. REX JOSEPH says:

OBVIOUSLY 142857
THIS IS HOW I GUESSED THE ANSWER;
ACCORDING TO THE QUESTION WHEN THE NUMBER IS ADDED AFTER 6 TIMES THE ANSWER IS 999999;IF THE NUMBER WERE ADDED IN DECIMAL THE ANSWER WOULD BE 0.999999 APPROXIMATELY 1
THERE FORE USING THE 1 ST CONCLUSION I AND 1/7*7=1
WHICH IS 142857

5. REX JOSEPH says:

THIS IS HOW I GUESSED IT;
ACCORDING TO THE QUESTION AFTER THE 6 TH ADDITION THE NUMBER WE GET IS 999999;
IF DIVIDED BY 100000 WE GET O.999999 APPROXIMATELY 1
THEREFORE 1/7*7=1
CORRELATING IT WITH THE 1ST CONCLUSION WE GET THE NUMBER TO BE 1/7*1000000=142857

6. athira says:

thanks for this nice explanation. try to add more another examples for cyclic numbers

7. vishal palapure says:

how to get that number..?

8. SmiluThomas says:

Take the number 142857 and multiply it by any number from 2 to 6. The result always has the same digits in the same order, if we say the first digit comes after the last.

For instance, we have 142857 * 2 = 285714. Note that in this number, just like in 142857, the digit 1 is followed by 4, which is followed by 2, which is followed by 8, which is followed by 5, which is followed by 7, which is followed again by 1. Such an arrangement of digits is called a cyclic permutation. For this reason, the number 142857 is called a cyclic number.

The other products, with the same property, are
3 * 142857 = 428571,
4 * 142857 = 571428,
5 * 142857 = 714285, and
6 * 142857 = 857142.

What about 7 * 142857? If you perform this multiplication, you’ll get another surprise, namely 142857 * 7 = 999999!

1. Very nicely explained. Appreciate your knowledge and observation. Keep commenting!!

2. athira says:

thank you smilu

9. khushboo says:

hey how did you get this number>??? ðŸ™‚

1. shravan kumar says:

divide 999999 by 7 =142857

10. Mohit says:

Correct

(142857)n