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The largest factorial in a 32 bit unsigned integer is 12!, which is 479,001,600. The largest factorical in a 64 bit unsigned integer is 20!, which is 2,432,902,008,176,640,000. Anything larger will overflow, and give wrong results. To go larger than that, you need to perform arithmetic digit by digit, or group by group, multiplying and carrying. Its the same as doing it on a piece of paper. You could create an array of digits and provide routines to multiply and carry. You could implement this as a linked list, making the length not preset. The elements do not have to be just digits - they could be larger, say 16 bit integers - so long as the largest possible operation would not result in an overflow.

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