Latest TCS Aptitude Question SOLUTION: (1!+2!+3!.........+50!)is divided by 5 then what wil b the remainder

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(1!+2!+3!.........+50!)is divided by 5 then what wil b the remainder

Asked In TCS nidhi kumari (11 years ago)

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Dr.Dipin Singh  (11 years ago)

(1!+2!+3!.........+50!)is divided by 5 then what wil b the remainder

The remainder will be same as (1!+2!+3!+4!)is divided by 5 .
(1!+2!+3!+4!)=1+2+6+24=33
when 33 is divided by 5, remainder is 3.
So when (1!+2!+3!.........+50!)is divided by 5 then remainder is 3.

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ankur shrivastava  (11 years ago)

always take the sum till the even term since 50th term is naturally even, i.e. 1!+2! or 1!+2!+3!+4! likewise..
so if we take, 1!+2!+3!+4! = 33
now, 33/5 leaves a remainder 3.
Hence, 3 is the desired ans.

Is this solution Helpfull? Yes (13) | No (1)  

shilpa  (11 years ago)

We just need to find which smallest factorial’s value is 5 or is a multiple of 5. Because any multiple of 5 divided by 5 leaves a remainder of zero.
We know that value of 5! is 120. If 5! = 120, it is guaranteed that all the factorials ahead of it will be a multiple of 5 as n! = n × (n – 1)! .
So, all the factorials starting from 5! onwards when divided by 5 will leave a remainder of zero. So. Our answer is dependent on the first 4 terms.
So, when (1! + 2! + 3! + 4!) ÷ 5=(1+2+6+24)/5 the remainder is 3.

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shilpa  (11 years ago)

soln not clear...any other way?

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shyamlesh dash  (11 years ago)

153 will be the remainder and 153/5=3 as remander 1 to 5 factorial will be the possible remainder rest all will be divisible by 5
any other questions or doubts u have pls mail me to shyamleshd@gmail.com

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harshita  (11 years ago)

The remainder will be same as (1!+2!+3!+4!)is divided by 5 .

WHY SO ?????????????????

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rajasekhar reddy  (11 years ago)

not clear can u explain in a clear way?

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