Write 1111......(243 times) i.e. a 243 digit number with all
Prove that it is divisible by 243.
Answers were Sorted based on User's Feedback
Answer / guest
Prove it using the mathematical induction.
First here are a couple of things to note:
 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.
 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).
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 )
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 ?||8 Yes||0 No|
Answer / madman042262
1111....n times(n=243) divided by 243
.............. 1n/243 where addition of 243 is 9
___________________________________________is this correct?
|Is This Answer Correct ?||1 Yes||1 No|
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||7 No|
A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says "At most n of te statements on this sheet are false". Which statments are true and which are false? A. The odd numbered statements are true and the even numbered are false. B. The even numbered statements are true and the odd numbered are false. C. All statements are true.
If you look at a clock and the time is 3:15. What is the angle between the hour and the minute hands? ( The answer to this is not zero!)
In the village called TALAJA, only three TV channels are available - Moon Plus, Mony and Mee TV. Out of 4000 TV viewers in the village, 1500 watch Moon TV, 2000 watch Mony and 2500 watch Mee TV. Amongst these, 500 viewers watch Moon Plus and Mony, 800 watch Moon Plus and Mee TV, and 1000 watch Mony and Mee TV. How many viewers watch all three channels?
In a college, the science department has three disciplines. In total, 280 students study chemistry, 254 students study physics and 280 students study biology. 97 students study both chemistry and physics, 138 students study both physics and biology, 152 students study both chemistry and biology. 73 students study all three disciplines. Can you determine how many students there are in the science department?
Hi Friends, Myself shiwani i had 11 years gap in my study and rite now i am 26 years,i enrolled myself in b.com and rite now i am in my second year and also pursuing CS(company secretary)and doing job in accounts department drawing 25000/-p.m,after completing my graduation and some level of cs module,would like to apply in mnc,would it matter to them that i had 11 years gap in study,kindly please help,me worried alot.
Outside a room there are three light switches. Each switch is connected to a different light bulb inside the room. Each of the three switches can be either 'ON' or 'OFF'. You are allowed to set each switch the way you want it, once, and then enter the room. Your task is to then determine which switch controls which bulb. How can you do it?
There is a perfect sphere of diameter 40 cms. resting up against a perfectly straight wall and a perfectly straight floor i.e. the wall and the floor make a perfect right angle. Can a perfect sphere of diameter 7 cms. pass through the space between the big sphere, the wall and the floor? Support your answer with valid arguments. Don't submit just "Yes" or "No".
in a family there are 5 members viz. parents and 3 children. the member are A,B,C,D AND E out of which 2 are males and 3 are females. A has 3 childerns, 2 daughters and 1 son. c in B's son. A in D's father. 1.how is E related to B? 2.who is D's mother? give me solution plese.
5+3+2=151012 9+2+4=183662 8+6+3=482466 5+4+5=202504 7+2+5=?
1.At the recent web developres bowling match,two ganes were played.Kiev beat stuart in both games;also Richard beat John in both games.The winner in game1 second in game2.Richard won game2 and John beat stuart in game1.No player got the same placing twice.Can you determine who finished where in each game?
iwant to know which type of questions were coming in tcs company
In how many iterations can we find one coin that is heavier than the others out of 8 coins?and how ?please reply