G = gcd(A,B) returns
the greatest common divisors of the elements of A and B.
The elements in G are always nonnegative, and gcd(0,0) returns 0.
This syntax supports inputs of any numeric type.

[G,U,V]
= gcd(A,B) also returns the Bézout
coefficients, U and V, which
satisfy: A.*U + B.*V = G. The Bézout coefficients
are useful for solving Diophantine equations. This syntax supports
double, single, and signed integer inputs.

Find the greatest common divisor and a pair of Bézout coefficients for 30 and 56.

[g,u,v] = gcd(30,56)

g =
2
u =
-13
v =
7

u and v satisfy the Bézout's identity, (30*u) + (56*v) = g.

Rewrite Bézout's identity so that it looks more like the original equation. Do this by multiplying by 4. Use == to verify that both sides of the equation are equal.

(30*u*4) + (56*v*4) == g*4

ans =
logical
1

Calculate the values of and that solve the problem.

A,B — Input values scalars, vectors, or arrays of real integer values

Input values, specified as scalars, vectors, or arrays of real
integer values. A and B can
be any numeric type, and they can be of different types within certain
limitations:

If A or B is
of type single, then the other can be of type single or double.

If A or B belongs
to an integer class, then the other must belong to the same class
or it must be a double scalar value.

A and B must be the same
size or one must be a scalar.

G — Greatest common divisor real, nonnegative integer values

Greatest common divisor, returned as an array of real nonnegative
integer values. G is the same size as A and B,
and the values in G are always real and nonnegative. G is
returned as the same type as A and B.
If A and B are of different
types, then G is returned as the nondouble type.

U,V — Bézout coefficients real integer values

Bézout coefficients, returned as arrays of real integer
values that satisfy the equation, A.*U + B.*V = G.
The data type of U and V is
the same type as that of A and B.
If A and B are of different
types, then U and V are returned
as the nondouble type.