Latest TCS Aptitude Question SOLUTION: what is the remainder if 100! divided by 97^2?

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(#M40011792) TCS question Keep an EYE

what is the remainder if 100! divided by 97^2?

Asked In TCS Payal Shrivastava (11 years ago)

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soumik banerjee  (11 years ago)

as 100!=100*99*98*97..../97*97
in 100! one 97 is divided by 97*97
so 1 97 is left for 97*97 it will be only 97
now 100*99*98*96....(as 97 got cancled) when divided by 97 reminder will be 3
bcoz their will always last 2 tearm is 00 for 100*99*98*96.....
consider 100*98=9800 when divided by 97 reminder is 3
so answer will be 3 when 100! divided by 97^2

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jaya  (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

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vasu  (11 years ago)

soumik u r wrong ,for xample if u conside 200 which has 00, has a remainder of 2

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soumik banerjee  (11 years ago)

vasu pls divide 200 by 97 u will get reminder is 6 and it is multiple of 3. now if u consider the whole 100! thn answer will be 3.

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kajal sharma  (11 years ago)

@jaya i got 1,2 nd and the last line,, but why u calculated 3*2*1 mod 97

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