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# gcd(+Number1, +Number2, -U, -V, -GCD)

Unifies GCD with the Greatest Common Divisor of Number1 and Number2, and gives appropriate coefficients U and V for the corresponding Bezout equation

Number1
  Integer.
Number2
  Integer.
U
  Output: integer.
V
  Output: integer.
GCD
  Output: integer.

## Description

The Greatest Common Divisor operation is only defined on integer arguments.

In coroutining mode, if Number1 or Number2 are uninstantiated, the call is delayed until these variables are instantiated.

The Bezout equation is Number1*U + Number2*V = GCD. These coefficients are calculated by an extended version of Euclid's algorithm.

### Modes and Determinism

- gcd(+, +, -, -, -) is det

### Exceptions

(4) instantiation fault
  Number1 or Number2 is not instantiated (non-coroutining mode only).
(5) type error
  Number1 or Number2 is a number but not an integer.
(24) number expected
  Number1 or Number2 is not of a numeric type.

## Examples

    Success:
          gcd(9, 15, 2, -1, 3).
          gcd(-9, 15, -2, -1, 3).
          gcd(2358352782,97895234896224,U,V,G).  % gives U = 2130001290117, V = -51312962, G = 6

    Error:
          gcd(A, 2, U, V, G).           (Error 4).
          gcd(1.0, 2, U, V, G).         (Error 5).
          gcd(4 + 2, 2, U, V, G).       (Error 24).

## See Also

gcd / 3, lcm / 3, is / 2