MuPAD Pro Computing Essentials - Examples 

Example 9.1 - Checking Factorials

How to check if a given integer n is the factorial of another integer? Here is the procedure doing it.

isfactorial:= proc(n:Type::PosInt)

local i;
begin
   i:=2;
   repeat
      if (n mod i = 0) and (n div i <>1) then
         n:=n div i;
         i:=i+1
      elif i=n then
         return(TRUE)
      else
         return(FALSE)
      end
   until FALSE end
end:

isfactorial(479001600)

true

12!

479001600

Now, we can use the procedure in a more bulky way. Let us check which numbers starting from 1 to 1000000 are factorials.

for n from 1 to 1000000 do
   if isfactorial(n) then
      print(Unquoted,expr2text(n)." is factorial number")
   end
end: