Latest TCS Aptitude Question SOLUTION: what is the remainder when 100! is divided by 97^2? 1.582 2.8148 3.1261 4.8827

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what is the remainder when 100! is divided by 97^2?
1.582 2.8148 3.1261 4.8827

Asked In TCS sweta shaw (11 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

kajal sharma  (11 years ago)

first understand dis
(6*10*55)/9
remainder of this is 6. there r two ways to calculate this
1--- 6*10*55 ie 3300 mod 9 = 6
2--- 6 mod 9 =6
10 mod 9 =1
55 mod 9=1
thn multiply all the rem n u get the ans ie 6

in case of 97^2
100*99*98*97*96! / 97^2
97 will b cancel out
100*99*98*96 ! / 97
nw find out remainder individually
100 % 97 =3
99 % 97 =2
98 % 97=1
and acc to wilson theorem
if p is a prime no thn (p-1)! mod p =-1
here 97 is a prime no so
96!% 97 = -1 or 96
so multiply all the rem
3 * 2*1* 96 mod 97 = 576 mod 97 = 91
nw multiply 91 with 97 so we get
91*97= 8827

Is this solution Helpfull? Yes (28) | No (4)  

Lovejeet Singh  (11 years ago)

Wilson Theorem ???
How does dat come by ??
and how to apply it ??
Wilson Theorem is for Prime No. and 96 is NOT a prime ...
Please elaborate a bit more !!!
Thx !!

Is this solution Helpfull? Yes (10) | No   

Smita  (11 years ago)

100*99*98*97*96! mod 97^2 (applied wilson theorm for 96!)

cancel out 97 from numerator and denominator

3*2*1*96 mod 97

576 mod 97

91 mod 97

mos rem is 97*91=8827

Is this solution Helpfull? Yes (8) | No (9)  

Garima  (11 years ago)

8827 is the remainder when 100! is divided by 97^2.

Is this solution Helpfull? Yes (4) | No (1)  

Palash Bansal  (10 years ago)

@kajal sharma
plzz xplain, why u multiplied by 97 in last line? i.e 91*97 :/

Is this solution Helpfull? Yes (3) | No   

Lovejeet Singh  (11 years ago)

Please give the Explanation !!!!

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

Smita  (11 years ago)

97 is a prime number.

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

kajal sharma  (11 years ago)

@smita pls help us to understand the solution
explain why u did this
3*2*1*96 mod 97

Is this solution Helpfull? Yes | No (2)  

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