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Problem # 28 : Factorials
The factorial of a number is defined as the product of all numbers between 1 and the number, including them both.
So the factorial of 3 = 3 x 2 x 1 = 6, while that of 5 = 5 x 4 x 3 x 2 x 1 = 120. (Factorials of negative numbers are not defined, while that of 0 is defined as 1). The factorial operation is represented by an exclamation mark (!). Thus the factorial of 3 is represented by 3! = 12.
Most calculators cannot generate the factorial of large numbers (say greater than 20) accurately, ie, they can just give the first few digits correctly. Try finding 20! with any calculator, even the one that comes with Windows (not that I wish to imply Windows has some sort of superior calculator :-). You won't get many accurate digits.
The task is to find, accurately, the factorials of numbers which them calculators cannot compute. So write a program which returrns the factorial of numbers less than 60. Use a sub-routine, function, whatever you want. No technical specs for your program in this problem. (Actually, go for numbers greater than 60. The upper limit would probably be a function of the limits of your compiler. My QBasic program could find out 100!, didn't try higher numbers. C++ would obviously be able to handle even larger numbers faster).
Sample Output
Use this to check your program.
| 0! | = | 1 |
| 3! | = | 6 |
| 7! | = | 5040 |
| 15! | = | 1307674368000 |
| 20! | = | 2432902008176640000 |
| 21! | = | 51090942171709440000 |
| 22! | = | 1124000727777607680000 |
| 30! | = | 265252859812191058636308480000000 |
| 31! | = | 8222838654177922817725562880000000 |
| 32! | = | 263130836933693530167218012160000000 |
| 33! | = | 8683317618811886495518194401280000000 |
| 34! | = | 295232799039604140847618609643520000000 |
| 35! | = | 10333147966386144929666651337523200000000 |
| 36! | = | 371993326789901217467999448150835200000000 |
| 47! | = | 258623241511168180642964355153611979969197632389120000000000 |
| 48! | = | 12413915592536072670862289047373375038521486354677760000000000 |
| 49! | = | 608281864034267560872252163321295376887552831379210240000000000 |
| 50! | = | 30414093201713378043612608166064768844377641568960512000000000000 |
| 51! | = | 1551118753287382280224243016469303211063259720016986112000000000000 |
| 52! | = | 80658175170943878571660636856403766975289505440883277824000000000000 |
| 53! | = | 4274883284060025564298013753389399649690343788366813724672000000000000 |
| 55! | = | 12696403353658275925965100847566516959580321051449436762275840000000000000 |
| 56! | = | 710998587804863451854045647463724949736497978881168458687447040000000000000 |
| 57! | = | 40526919504877216755680601905432322134980384796226602145184481280000000000000 |
| 58! | = | 2350561331282878571829474910515074683828862318181142924420699914240000000000000 |
| 59! | = | 138683118545689835737939019720389406345902876772687432540821294940160000000000000 |
| 60! | = | 8320987112741390144276341183223364380754172606361245952449277696409600000000000000 |
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