Computing the Greatest Common Divisor of Two Positive Integers

Problem Statement

The Greatest Common Divisor, GCD for short, of two positive integers can be computed with Euclid's division algorithm. Let the given numbers be a and b, a >= b. Euclid's division algorithm has the following steps:

  1. Compute the remainder c of dividing a by b.
  2. If the remainder c is zero, b is the greatest common divisor.
  3. If c is not zero, replace a with b and b with the remainder c. Go back to step (1).
Write a program that reads in two integers and computes their greatest common divisor. Note that these two input could be in any order.


! ---------------------------------------------------------
! This program computes the GCD of two positive integers
! using the Euclid method.  Given a and b, a >= b, the
! Euclid method goes as follows:  (1) dividing a by b yields
! a reminder c; (2) if c is zero, b is the GCD; (3) if c is
! no zero, b becomes a and c becomes c and go back to
! Step (1).  This process will continue until c is zero.
! ---------------------------------------------------------

PROGRAM  GreatestCommonDivisor

   INTEGER   :: a, b, c

   WRITE(*,*) 'Two positive integers please --> '
   READ(*,*)  a, b
   IF (a < b) THEN       ! since a >= b must be true, they
      c = a              ! are swapped if a < b
      a = b
      b = c

   DO                    ! now we have a <= b
      c = MOD(a, b)      !    compute c, the reminder
      IF (c == 0) EXIT   !    if c is zero, we are done.  GCD = b
      a = b              !    otherwise, b becomes a
      b = c              !    and c becomes b
   END DO                !    go back

   WRITE(*,*) 'The GCD is ', b

END PROGRAM  GreatestCommonDivisor
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