17: recursion.cpp) Write two recursive integer functions. The first function should calculate factorials using the definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too large it should be able to detect integer overflow before it happens. The next function should calculate the greatest common factor (gcf) of two numbers. If the second number is zero, then the gcf is the other number. Otherwise, the gcf of a and b is the same as the gcf of b and a mod b.

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Please code using C++ and only use the headers <iostream> and <limits.h>. Any other additional headers will not be accpepted. Thank you!

17: recursion.cpp) Write two recursive integer functions.
The first function should calculate factorials using the
definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too
large it should be able to detect integer overflow before it
happens. The next function should calculate the greatest
common factor (gcf) of two numbers. If the second number
is zero, then the gcf is the other number. Otherwise, the gcf
of a and b is the same as the gcf of b and a mod b.
Transcribed Image Text:17: recursion.cpp) Write two recursive integer functions. The first function should calculate factorials using the definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too large it should be able to detect integer overflow before it happens. The next function should calculate the greatest common factor (gcf) of two numbers. If the second number is zero, then the gcf is the other number. Otherwise, the gcf of a and b is the same as the gcf of b and a mod b.
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