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?
Leave your answers below. We will provide the answer if you ask for 
You may also like:
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
Get Maths Tricks by Email
Recent Comments
A, B and C can do a piece of work in 40, 60 and 120... – 07Feb12
as a night watchman he is not supposed to sleep during the night . as... – 06Feb12
ramlal is a night watchman and he is sleep on duty therefor boss fire him,... – 06Feb12
Dear, It is good..... But I was already given this question on 06-12-2011 at 11.08... – 05Feb12
he rewarded the watchman because watchman saved his life by warning him that the plane... – 05Feb12
Most Popular
- 100% Finding Cube Root – Vedic Maths Way
- 67% Shortcut to Find Square of a Number
- 57% Shortcut Method for Multiplication
- 56% Shortcut to find the Cube of a number
- 53% Squaring any 2-digit number
- 49% Divisibility Rule of 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47
- 45% Division in Vedic Mathematics
- 45% Herons Method of Finding Roots
- 43% You can make a difference
- 41% Quicker Maths by M Tyra
- 40% Quick calculations for extremely large numbers
- 39% Divisibility Rules for 7 , 11 and 13
- 37% How to convert from decimal to other number systems
- 36% Quick Multiplication up to 20 x 20
- 35% Logical Reasoning Books
May 5th, 2011 - 16:24
the next number is 0588235294117647 which on the 16th multiplication will give 9999999999999999
March 5th, 2011 - 18:23
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
1/7*1000000 IS THE ANSWER;
WHICH IS 142857
March 5th, 2011 - 18:17
OBVIOUSLY THE ANSWER IS 142857
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
November 29th, 2010 - 20:53
thanks for this nice explanation. try to add more another examples for cyclic numbers
September 14th, 2010 - 13:21
how to get that number..?
August 24th, 2010 - 19:49
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!
August 25th, 2010 - 16:55
Very nicely explained. Appreciate your knowledge and observation. Keep commenting!!
November 29th, 2010 - 20:54
thank you smilu
March 28th, 2010 - 19:55
hey how did you get this number>???
February 5th, 2010 - 00:42
hi
January 31st, 2010 - 17:44
Correct
(142857)n
January 31st, 2010 - 12:08
142857