Test each possible positive divisor directly:
PROCEDURE divisors(n: INTEGER): INTEGER;
VAR i, count: INTEGER;
BEGIN
  i := 1; count := 0;
  WHILE i <= n DO
    IF n MOD i = 0 THEN count := count + 1 END;
    i := i + 1
  END;
  RETURN count
END divisors;
For , the loop invariant is and count . Testing adds exactly the next possible divisor. The loop variant decreases, and the divisor in MOD is always positive. At exit the interval contains every positive divisor. This computes the divisor function using remainder operations, time, and auxiliary space.

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