Ada compilation warnings

If I compile your code with -gnatl (listing of source with error messages in line), it gives

 1. with Ada.Text_IO, Ada.Integer_Text_IO;
 2. use  Ada.Text_IO, Ada.Integer_Text_IO;
 3.
 4. procedure factorial_ada is
 5.
 6.     n, i : Integer;
           |
    >>> warning: variable "i" is never read and never assigned

 7.     output : Integer := 1;
 8.
 9. begin
10.     Put_Line("Enter the number to be taken factorial of: ");
11.     Get(n);
12.
13.    -- Begin Loop
14.     for i in 2..n
            |
    >>> warning: for loop implicitly declares loop variable
    >>> warning: declaration hides "i" declared at line 6

15.     loop
16.         output := output * i;
17.     end loop;
18.
19.     Put("Factorial of ");
20.     Put(n);
21.     Put(" is ");
22.     Put(output);
23.
24. end factorial_ada;

The warnings at line 14 remind you that (ARM 5.5(11))

An object_declaration should not be given for a loop parameter, since the loop parameter is automatically declared by the loop_parameter_specification. The scope of a loop parameter extends from the loop_parameter_specification to the end of the loop_statement, and the visibility rules are such that a loop parameter is only visible within the sequence_of_statements of the loop.

The warning at line 6 is telling you that this i (an "object declaration", in ARM-speak) has nothing to do with the i at line 14.

This is similar to the C++ rules: writing

#include <stdio.h>
int main() {
  int i;
  int output = 1;
  int n = 12;
  for (int i = 2; i <= n; i++) {
    output *= i;
  }
  printf("factorial %d is %d\n", i, output);
  return 0;
}

results in

$ g++ hk.cc -Wall
hk.cc: In function 'int main()':
hk.cc:9:9: warning: 'i' is used uninitialized in this function [-Wuninitialized]
    9 |   printf("factorial %d is %d\n", i, output);
      |   ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~