Latest TCS Aptitude Question SOLUTION: Find the last non zero digit of 96! a) 2 b) 4 c) 6 d) 8

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(#M40012192) TCS question Keep an EYE

Find the last non zero digit of 96!
a) 2
b) 4
c) 6
d) 8

Asked In TCS Lovejeet Singh (12 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

lala  (12 years ago)

by my frnd ammir soln
The Algorithm for finding this is :
Lets say D(N) denotes the last non zero digit of factorial, then the algo says
D(N)=4*D[N/5]*D(Unit digit of N)[If tens digit of N is odd]
D(N)=6*D[N/5]*D(Unit digit of N)[If tens digit of N is even]; Where [N/5] is greatest Integer Function (floor)
Also,
D(1)=1 D(2)=2 D(3)=6 D(4)=4 D(5)=2 D(6)=2 D(7)=4 D(8)=2 D(9)=8

D(96)
= 4*D[96/5]*D(6)
= 4*D(19)*D(6)
=4*{4*D(19/5)*D(9)}*D(6)
4*{4*D(3)*8}*2
4*4*6*8*2
1536
so last digit is 6

Is this solution Helpfull? Yes (14) | No   

aamir  (12 years ago)

The Algorithm for finding this is :
Lets say D(N) denotes the last non zero digit of factorial, then the algo says
D(N)=4*D[N/5]*D(Unit digit of N)[If tens digit of N is odd]
D(N)=6*D[N/5]*D(Unit digit of N)[If tens digit of N is even]; Where [N/5] is greatest Integer Function (floor)
Also,
D(1)=1 D(2)=2 D(3)=6 D(4)=4 D(5)=2 D(6)=2 D(7)=4 D(8)=2 D(9)=8

D(96)
= 4*D[96/5]*D(6)
= 4*D(19)*D(6)
= 4*(4*D[19/5]*D(9))*2
= 4*(4*D(3))*2
= 4*4*6*2
= 192
Ans = 2

Is this solution Helpfull? Yes (10) | No (7)  

Gaurav Bhadama  (12 years ago)

4*d(96/5)*d(6)

4*d(19)*d(6)

4*2*2 = 16=6

last non zero digit of 96! is 6

>

Is this solution Helpfull? Yes (6) | No (3)  

jasveer   (12 years ago)

aamir u don't write the value of d(9) at last step when u put it the last non zero digit is 6

Is this solution Helpfull? Yes (6) | No   

goldy  (12 years ago)

from calculating 1 to 91 we have 1,11,21,31,,,,,91 multiply their last digits u will get 1
from calculating 2 to 92 we have 2,,12,22,32,,,,,92 multiply their last digits u will get (2)^10=2048=last digit=8
from calculating 3 to 93 we have 3,13,23,33,,,,,93 multiply their last digits u will get (3)^10=177147=last digit=7
from 4,14,,,,,,,,,94 last digit is=4
from 5,15,25,,,,,,95 last digit is=5
from 6,16,26,,,,,,96 last digit is=6
but now in 7,17,27,,,,,,87 last digit is in (7)^9=282475249=9
for the series of 8 last digit=4
for the series of 9 lastdigit is=1
now multiply all the last digits i;e
1*8*7*4*5*6*9*4*1=241920
thus last digit is 2...

Is this solution Helpfull? Yes (5) | No (6)  

k.m  (11 years ago)

guys see
96!=96*95*94..........
since if we multiply last digits of 96 and 95 i.e 6*5=30 we got 0 in end similarly 95*94 i.e 5*4=20 we got 0 in end now if we multiply 94*93 i.e 4*3=12 last digit is 2 so it is last non zero digit. so answer is 2

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Vikas  (12 years ago)

i cant understand it gaurav. plz explain

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