Latest TCS Aptitude Question SOLUTION: what is the remainder when 123456789..........44 is divided by 45?

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(#M40029199) TCS Numerical Ability question Keep an EYE

what is the remainder when 123456789..........44 is divided by 45?

Asked In TCS pre (10 years ago)

Solved RAKESH Read Solution (18)

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sami wardhan karn  (10 years ago)

123456789..........44/45
123456789..........44/(5*9)
sum of termss in given no. is =44*(44+1)/2=22*45,which is divisible by 9
so 123456789..........44 is divisible by 9
hence we will have 6 in the unit place after we divide 1234567....44 by 9.
now only 5 is left in the dinominator i.e. .......6/5
hence the remainder when divided by 5 is 1

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RAKESH  (10 years ago) Best Solution

sorry for the last answer 123456789..........44/45
123456789..........44/(5*9)
sum of termss in given no. is =44*(44+1)/2=22*45,which is divisible by 9
so 123456789..........44 is divisible by 9
since 123456789..........44 is divisible by 9,there must be 6 at unit place of quoitient(there is 4 at the unit place of number,since it is divisible by 9 so last two term should be 54 as table of 9 =9,18,27,36,45,54,63,72,81,90)
last term of the quotient is 6
now it is divided by 5
so remainder will be 1

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RAKESH  (10 years ago)

123456789..........44/45
123456789..........44/(5*9)
sum of termss in given no. is =44*(44+1)/2=22*45,which is divisible by 9
so 123456789..........44 is divisible by 9
123456789..........44/5 gives remainder 4
so 123456789..........44/5*9 will give a remainder 4*9=36
so 36 is the ANS

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PRADEEP MUKHERJEE  (10 years ago)

9 is the ansr

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monia prasad  (10 years ago)

0 is d r8 ans

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monia prasad  (10 years ago)

0 is d r8 ans

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monia prasad  (10 years ago)

ans is 9.find the sum of all digit using n(n+1)/2 where n=44 which can be divided by 9 as the 9 is factor of 45 gives rem =1 so 1*9=9

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Arka Chakraborty  (10 years ago)

9 is the answer

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Manas Dutta  (10 years ago)

Ans must be 9...because as we divide dis no by 9 and get the unit digit 6.then we find out the remainder 1..so we hav to multiply 9 with it..answer should be 9..

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Saloni Singh  (10 years ago)

@rakesh isnt the term 22*45 directly divisible by 45 resulting in NO remainder??

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Saloni Singh  (10 years ago)

@sami : can u xplain dis part??
hence we will have 6 in the unit place after we divide 1234567....44 by 9.
now only 5 is left in the dinominator i.e. .......6/5
hence the remainder when divided by 5 is 1

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alok kumar  (10 years ago)

123456789..........44/45
123456789..........44/(5*9)
sum of termss in given no. is =44*(44+1)/2=22*45,which is divisible by 9
so 123456789..........44 is divisible by 9
hence we will have 6 in the unit place after we divide 1234567....44 by 9.
now only 5 is left in the dinominator i.e. .......6/5
hence the remainder when divided by 5 is 1
but we have to get the remainder when we divide the no by 45 hence multiply the remainder obtained above by 9 again so remainder is 9*1 =9
#remember sum of digits taken as 1+2+3+....41+42+43+44 will yield the same divisibility test for 9 as 1+2+3+4+....4+1+4+2+4+3+4+4 :)

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payaljain  (10 years ago)

what r u doing guys
it is sum of digits not sum of nos so u cant use n(n+1)/2
sum of digits is 45*4+1*10+2*10+3*10+4*4+(1+2+3+4)=260=2+6=8 is remainder not divided by 9

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Prabal Gupta  (10 years ago)

19, last number is 44 which can't be divided by 45. Therefore,the previous number i.e., 43 has to be taken into consideration. Since, 44 is a two digit number, we need to take 3 of 43, therefore the number becomes 344. Now u get 344/45 and the remainder is 29

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Md Yeanur Mallick  (10 years ago)

The ans is= 0
as the no has contan (12.......45.......44)/45=0

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Ajay Poshak  (10 years ago)

Given number contains the 9 and 5 so the divisor 45 is fully divisible by given number.
Thus remainder will be zero.

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MAHASIN RAHAMAN  (10 years ago)

the remainder will be 4..
see, 45=3*3*5 (the highest factr is 5)
so we must chck the number divisible by 5 or not,, as the whole number ends will 44 ,,so its 4 remaining...

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kaustav das  (10 years ago)

The number is divisible by 9 as sum of the numbers are divisible by 9...then if we subtract 9(.i.e the lowest multiple of 9 that should be subtracted )to get last digit as 35 which means the no is divisible by 5..so ans 9

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