`gcd`

Greatest common divisor of integers.

Category: Mathematics > Elementary Math

Syntax

G = gcd(A, B)

Returns the largest positive integer that divides both A and B, element by element.

Description

The computation uses the Euclidean algorithm: replace the pair (a, b) by (b, mod(a, b)) until the second number is zero. Signs are ignored, since the divisor is always taken positive.

To reduce a fraction p/q to lowest terms, divide both by gcd(p, q). The least common multiple is related by lcm(a, b) = abs(a*b)/gcd(a, b).

Input arguments

A, B: Integer-valued arrays of compatible sizes. A scalar is expanded to match an array.

Output arguments

G: Array of nonnegative integers. gcd(0, 0) is 0, and gcd(0, n) is abs(n). Integer inputs of one class give a result of that class.

Example

Scalars and arrays

gcd(12, 18)
gcd([12 15 20], 5)
gcd(0, 7)

Output

ans = 6
ans = 1×3

     1     5     5
ans = 7

See also

lcm factor mod rat primes