Greatest common divisor
A = [-5 17; 10 0]; B = [-15 3; 100 0]; G = gcd(A,B)
G = 5 1 10 0
gcd returns positive values, even when the inputs are negative.
A = uint16([255 511 15]); B = uint16([15 127 1023]); G = gcd(A,B)
G = 15 1 3
Solve the Diophantine equation, 30x + 56y = 8 for x and y.
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 = 1
Calculate the values of x and y that solve the problem.
x = u*4 y = v*4
x = -52 y = 28
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.
Example: [20 -3 13],[10 6 7]
Example: int16([100 -30 200]),int16([20 15 9])
Example: int16([100 -30 200]),20
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
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.
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.
 Knuth, D. "Algorithms A and X." The Art of Computer Programming, Vol. 2, Section 4.5.2. Reading, MA: Addison-Wesley, 1973.