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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).
```