Write 1111......(243 times) i.e. a 243 digit number with all
1s.

Prove that it is divisible by 243.

Answers were Sorted based on User's Feedback



Write 1111......(243 times) i.e. a 243 digit number with all 1s. Prove that it is divisible by ..

Answer / guest

Prove it using the mathematical induction.

First here are a couple of things to note:

[1] A number whose digits add up to a multiple of three is
divisable by 3.

e.g. 369: 3+6+9=18: 1+8=9 which is a multiple of 3 hence 369
is divisable by 3.

[2] Whenever a number (X) is multiplied with another number
(Y) then the product (X*Y) will have all the factors of X as
well as all the factors of Y in its set of factors.

e.g. if X has factors of (1,P,Q,X) and Y has factors of
(1,Q,R,Y) then X*Y has factors of (1,P,Q,Q,R,X,Y).

Let

N = any series of digits (e.g. N=369)

D = the number of digits in N (e.g. if N=369 then D=3)

P = is a number constructed in the following way : a 1,
followed by (D-1) 0s, followed by another 1, followed by
(D-1) 0s, followed by another 1. (e.g. if N=369 then D=3 and
P would be 1001001) Note that P will always be divisible by 3.

Also, if we multiply N with P we are essentially repeating N
for (D-1) times.

e.g. if N=369 then D=3, P=1001001 and N*P=369369369

Let's start with N=111. It is clear that N is divisible by
3. (From [1])

Also, D=3 and P=1001001

N*P=111111111 (9 times)

The resulting number 111111111 must be divisible by 9 as N
and P both are divisible by 3.

Now, let's start with N=111111111. It is clear that N is
divisible by 9.

Also, D=9 and P=1000000001000000001

N*P=111111111... (27 times)

The resulting number 1111111... (27 times) must be divisible
by 27 as N is divisible by 9 and P is divisible by 3.

Repeat the same procedure for N=1111111... (27 times) The
resulting number 1111111... (81 times) must be divisible by
81 as N is divisible by 27 and P is divisible by 3.

Similarly, for N=1111111... (81 times) The resulting number
1111111... (243 times) must be divisible by 243 as N is
divisible by 81 and P is divisible by 3.

Thus, 1111111... (243 times) is divisible by 243.

Is This Answer Correct ?    19 Yes 1 No

Write 1111......(243 times) i.e. a 243 digit number with all 1s. Prove that it is divisible by ..

Answer / madman042262

1111....n times(n=243) divided by 243
>>
2+4+3=9
2+4+3=9
.............. 1n/243 where addition of 243 is 9
.............. 1(9)/9=1?
___________________________________________is this correct?

Is This Answer Correct ?    1 Yes 2 No

Write 1111......(243 times) i.e. a 243 digit number with all 1s. Prove that it is divisible by ..

Answer / karthik

factors of 243 is 3^5(3*3*3*3*3) (i.e) 3 is the divident of 243.
.
. . the number (111111.....(243 ones)) is also
divisable by 243.

why i am saying is the total addition of a given
number is divisible by 3.so, definately i say that the given
number is divisal by 243(it is also divisable by 3).

Is This Answer Correct ?    2 Yes 10 No

Post New Answer

More Puzzles Interview Questions

1) You have 8 coins. 3 of them weigh x units, 3 y units, 1 a units and 1 b units. They are all mixed and look identical. You have to find the lightest coin in minimum number of weighing .

9 Answers   Bhel, Mechanical, Microsoft, Oracle,


agar mein aapko ek pen gift du aur aapko kahu ki aap us pen se mere haato me kuch likho jo mujhe hamesa yaad rahe to aap kya likhoge?

13 Answers  


Imagine that u r driving a car from mysore to bangalore at a speed of 75mph.car no is KA-19 DB1955. distance between bangalore and mysore is 250 Km..... Now tell me wat s the date of birth of the driver............

25 Answers   ADP, AP, BPO, CTS, HOV Services, HSBC, Infosys, Prodapt, Vodafone,


A, B and C are three points on a straight line, not necessarily equidistant with B being between A and C. Three semicircles are drawn on the same side of the line with AB, BC and AC as the diameters. BD is perpendicular to the line ABC, and D lies on the semicircle AC. If the funny shaped diagram between the three semicircles has an area of 1000 square cms, find the length of BD.

1 Answers  


A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?

3 Answers  






X is a 6 letter word 1 2 and 5 6 letters are the same 3 4 is a day 1 2 5 6 is go away 1 2 3 6 is fat and X is an international celebrity .. What is X ?

6 Answers   Infosys,


if (x-a) power(degree) is 1 and (x-a)(x-b) power is 2 then (x-a)(x-b).........upto ...(x-z) power(degree) is how much?

9 Answers   BA Continnum Solutions, HCL, Wipro,


In Mr. Mehta's family, there are one grandfather, one grandmother, two fathers, two mothers, one father-in-law, one mother-in-law, four children, three grandchildren, one brother, two sisters, two sons, two daughters and one daughter-in-law. How many members are there in Mr. Mehta's family? Give minimal possible answer.

2 Answers  


Ek nadi ka Name Ek Ladki ka Name Ek PHOOL ka Name 3 sawalon ka jawab ek hi hona chahiye wo bhi Ek film ka Name hai...........

46 Answers   Ansor, Eagle, FGG, Ganga, Godavari, Infosys, JPSC Jharkhand Public Service Commission, Nilkamal, Parimal, Shani, Sola, SSC, Ugar,


Five friends with surname Batliwala, Pocketwala, Talawala, Chunawala and Natakwala have their first name and middle name as follow. 1. Four of them have a first and middle name of Paresh. 2. Three of them have a first and middle name of Kamlesh. 3. Two of them have a first and middle name of Naresh. 4. One of them have a first and middle name of Elesh. 5. Pocketwala and Talawala, either both are named Kamlesh or neither is named Kamlesh. 6. Either Batliwala and Pocketwala both are named Naresh or Talawala and Chunawala both are named Naresh. 7. Chunawala and Natakwala are not both named Paresh. Who is named Elesh?

2 Answers  


At University of Probability, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award. What percent chance is there that it will be a junior? Round to the nearest whole percent

2 Answers  


wo kya cheez hai jo saal me 1 baar mahine me 2 baar hafte me 4 baar aur din me 6 baar aati hai

39 Answers   AAA, Global Systems, Google, Human Resources, Infosys, IOCL, Matter and Co, Mind Tree, Prakash Industries, Samsung, Serco, Shani, Shreya Garments, Suman Industries, TNT, VIP, WhatsApp, YDS,


Categories