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Solution - Factorials

210202660512637835935172644211957133627043908720000167536756842728609276364870071276018632900069284700768301037938261101173961429020590768649673393745350229366900929723019237747008737725622726743681331817177398316310598929099640952146939184746561215434218580476712209164729840218710611141997608556081517114151978078529649675756198677900973955961088376590768187445187161362720223207506081889280736666374823205851569546732513468951411991741029659341762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000
210202660512637835935172644211957133627043908720000167536756842728609276364870071276018632900069284700768301037938261101173961429020590768649673393745350229366900929723019237747008737725622726743681331817177398316310598929099640952146939184746561215434218580476712209164729840218710611141997608556081517114151978078529649675756198677900973955961088376590768187445187161362720223207506081889280736666374823205851569546732513468951411991741029659341762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000

Other Ways to Solve

Factorials

Step-by-step explanation

1. Find the factorial

The factorial of 312 is the product of all positive integers less than or equal to 312:

312!=312·311·310·309·308·307·306·305·...·7·6·5·4·3·2·1=210202660512637835935172644211957133627043908720000167536756842728609276364870071276018632900069284700768301037938261101173961429020590768649673393745350229366900929723019237747008737725622726743681331817177398316310598929099640952146939184746561215434218580476712209164729840218710611141997608556081517114151978078529649675756198677900973955961088376590768187445187161362720223207506081889280736666374823205851569546732513468951411991741029659341762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000

Why learn this

There are more ways to arrange a deck of cards than there are atoms on Earth. In fact, if you were to shuffle a standard deck of fifty-two cards and lay them out in a row, it would probably be the first time in all of human history that exact arrangement has been laid out and the last time it ever will be. Such enormous numbers are hard to even imagine and, thanks to factorials, we do not have to try.

Factorials, which are expressed as a whole number followed by an exclamation point (for example: 10!), are used frequently in mathematics, mostly to determine the number of different combinations, or permutations, a set of things can have. In our card example, the factorial would be 52!, which is equal to roughly 8 with 67 zeros.
Look at the deck next time you decide to play a game of cards. Chances are you are holding something that has never existed in that exact way before and never will again.

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