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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*
- A variable of integer.
*V*
- A variable or integer.
*GCD*
- A variable or 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 )
Fail:
gcd(1, 2, U, V, 3.0).
Error:
gcd(A, 2, U, V, 6). (Error 4).
gcd(1.0, 2, U, V, 3.0). (Error 5).
gcd(4 + 2, 2, U, V, 12). (Error 24).

## See Also

gcd / 3, lcm / 3, is / 2