Quick !!!

what is the smallest prime number that doesn't divide 101 ! 101! ??


The answer is 103.

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1 solution

Adarsh Kumar
Sep 1, 2014

V E R Y S I M P L E Q U E S T I O N VERY\ SIMPLE\ QUESTION B E C A U S E 101 ! C O N T A I N S E V E R Y N U M B E R F R O M 1 T O 101 I T W I L L B E D I V I S I B L E B Y E V E R Y N U M B E R F R O M 1 T O 101. BECAUSE\ 101!\ CONTAINS\ EVERY\ NUMBER\ FROM\ 1\ TO\ 101\ IT\ WILL\ BE\ DIVISIBLE\ BY\ EVERY\ NUMBER\ FROM\ 1\ TO\ 101. S O F O R F I N D I N G T H E S M A L L E S T P R I M E W H I C H D O E S N T D I V I D E 101 ! I S T H E S M A L L E S T P R I M E T H A T I S G R E A T E R T H A N 101. SO\ FOR\ FINDING\ THE\ SMALLEST\ PRIME\ WHICH\ DOESN'T\ DIVIDE\ 101!\ IS\ THE\ SMALLEST\ PRIME\ THAT\ IS\ GREATER\ THAN\ 101. T H A T P R I M E I S 103. THAT\ PRIME\ IS\ 103. A N D B E C A U S E 103 I S A P R I M E , I T C A N O N L Y B E M A D E W H E N 1 A N D 103 A R E M U L T I P L I E D . AND\ BECAUSE\ 103\ IS\ A \ PRIME,\ IT\ CAN\ ONLY\ BE\ MADE\ WHEN\ 1\ AND\ 103\ ARE\ MULTIPLIED. S O T H E R E I S N O W A Y T H A T I T W I L L B E P R E S E N T I N T H E P R I M E F A C T O R I S A T I O N O F 101 ! SO\ THERE\ IS\ NO\ WAY\ THAT\ IT\ WILL\ BE\ PRESENT\ IN\ THE\ PRIME\ FACTORISATION\ OF\ 101!

t h i s i s m y f i r s t l a t e x s o l u t i o n . this\ is\ my\ first\ latex\ solution.

Adarsh Kumar - 6 years, 9 months ago

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FYI - To type equations in Latex, you just need to add around your math code, as opposed to all of the text.

Also, please refrain from typing in all caps, as that is internet-speak for "I AM SHOUTING AT YOU!"

Calvin Lin Staff - 6 years, 9 months ago

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Yes sir,I got it.Thanx.

Adarsh Kumar - 6 years, 9 months ago

thats good

math man - 6 years, 9 months ago

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t h a n x thanx a h e a d s t a r t t o m y l a t e x c h a p t e r a\ head\ start\ to\ my\ latex\ chapter

Adarsh Kumar - 6 years, 9 months ago

correct ...

math man - 6 years, 9 months ago

Good question. Thankx!

Suruthi Bhashini - 6 years, 9 months ago

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your welcome

math man - 6 years, 9 months ago

I didnt understand. :/ care to explain?

Suraj Iyyengar - 6 years, 9 months ago

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101! = 1x2x3x4x5x...x101 , so it is divisible by number 1 -101

math man - 6 years, 9 months ago

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