Latest TCS Aptitude Question SOLUTION: What is the last non zero digit of 96! ?

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What is the last non zero digit of 96! ?

Asked In TCS Pawan Ahuja (12 years ago)

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farhana begum  (12 years ago)

given :1*2*3*....96
first take 1st 10 digits
1*2*3*4*5*6*7*8*9*10
now ignore those which give a product of 10
thus take only 1*2*3*4*6*8*9
note that we havnt taken 2 and 5 as it gives a product of 10.similarly we ignored 10
now the product of 1 2 3 4 6 8 9 gives 8 in units place
every 10 digits set is taken and each set gives 8 digit i units place in the product of those 10 digits
now from 1 to 90 we have 8*8*....nine times
now for the above product we have 8 as units digit
Now find out the units digit for 91*92*93*94*95*96....again here we xclude 10
and we take non zero digit i.e 2
now 8*2 gives 6 in the units place
thus ans is 6

Is this solution Helpfull? Yes (20) | No (3)  

Bhavya Dubey  (12 years ago)

Given the word “Parrot”. Find the 20th word in dictionary order. can any one tell me how to solve this

Is this solution Helpfull? Yes (8) | No (2)  

Rajesh kumar  (12 years ago)

If we try to compute 96!
then
4*z(96/5)*z(6)
=4*z(19)*8
96!,Z(n) = {4 if tens digit is odd and 6 if tens digit is even) *
Z(n/5) * z(Units digit).=8*(4*z(19/5)*z(9))
=8*(4*z(3)*8)
=8*(4*6*8)
=1536 i.e last digit is 6

Is this solution Helpfull? Yes (6) | No   

Rajat Dadhich  (12 years ago)

the answer will be 6...

its difficult to xplain as it involves long theory

Is this solution Helpfull? Yes (3) | No   

Rahul singh  (12 years ago)

Z(n) denotes the last non zero digit in n!

Z(n) = 4 if tens digit is odd and 6 if tens digit is even
Z(n/5) * z(Units digit).

example

last digit of 96!

Z(96) = 6 * Z(96/5) * Z(6)
= 6 * z(19) * last non zero digit of 6!
= 6 * last non zero digit of 19! * last non zero digit of 6!
= 6 * by same process i got 2 * last non zero digit of (120)
= 6 * 2 * 2
= 24 (answer is the last digit ie 4)
= 4

Is this solution Helpfull? Yes (3) | No (4)  

Aparna Rakate  (12 years ago)

the ans is 6.
using formula 4*D(n/5)*D(unit place of 96)
4*D(19)*D(6)
4*[4*D(3)*D(9)]*D(6)
4*4*6*8*2
=1536
ans = 6

Is this solution Helpfull? Yes (3) | No (2)  

kavita dalmia  (12 years ago)

96! has numbers that are multiple of 5 and the rest.. rest of the numbers have 6 as their last digit only. numbers from 91 to 94 have 4.. so 6*4 =4 is the last digit for that group. now for 5 multiples write 5=5*1, 10=5*2 and so on till 95.. shift the 1 , 2,... 19 to the second group. giving 6 there too.. now what should be multiplied with 4 to give 4 as a last digit. either 1 or 6.. that is the answer.

Is this solution Helpfull? Yes (2) | No   

Prateek  (12 years ago)

ans is 6.

Is this solution Helpfull? Yes (1) | No   

Amit gupta  (12 years ago)

miss farhana forget 7 in his process...including 7 n then by repeating same procedure....i think answer will be 2

Is this solution Helpfull? Yes (1) | No (2)  

Vikrant Varshney  (12 years ago)

kavita plz give the solution more clear...
i cant understand this one

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prachitrivedi  (12 years ago)

ans is 2bcoz product of 91 92 93 94 96 gives unit digit 4 for remain semeas farhan 8*4=2

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