GCD

Return the greatest common divisor of two integers (non-negative, using the Euclidean algorithm).

Syntax

GCD(a, b)

Description

## Overview Returns the greatest common divisor (GCD) of two integers. The GCD is the largest non-negative integer that divides both inputs exactly. GCD is computed with the Euclidean algorithm, which runs in O(log(min(a, b))) time and is numerically exact. GCD is a foundational primitive for reducing fractions to lowest terms, computing LCMs, and performing modular arithmetic. It is symmetric (GCD(a, b) = GCD(b, a)) and sign-agnostic (GCD(-a, b) = GCD(a, b)). ## Behavior - Accepts INTEGER or BIGINT for both arguments. - Returns a non-negative integer of the promoted common type. - Returns NULL if either argument is NULL. - GCD(0, n) returns |n| and GCD(n, 0) returns |n|. - GCD(0, 0) returns 0 by convention. - Is symmetric and sign-agnostic. ## Numeric precision - For INTEGER and BIGINT, GCD is exact. - The Euclidean algorithm does not overflow for values within the integer type's range. - GCD does not accept DECIMAL or DOUBLE inputs; cast to INT if your values are integer-valued floats. ## Compatibility - Matches the PostgreSQL GCD scalar function. - Conforms to the standard mathematical definition of GCD.

Parameters

Name	Type	Description
a		Specifies the first integer operand. Negative values are accepted; the result uses the absolute values of the inputs.
b		Specifies the second integer operand. Negative values are accepted; the result uses the absolute values of the inputs.

Examples

-- Basic GCD
SELECT GCD(12, 8);  -- 4

-- Coprime numbers
SELECT GCD(7, 13);  -- 1

-- GCD with zero is the absolute value of the other argument
SELECT GCD(0, 5);  -- 5

-- Negative inputs produce a non-negative result
SELECT GCD(-12, 8);  -- 4

-- Both zero by convention is zero
SELECT GCD(0, 0);  -- 0

-- NULL propagation
SELECT GCD(NULL, 12);  -- NULL

Pitfalls

• GCD does not accept fractional types. Cast DECIMAL or DOUBLE to INT before calling, and be aware that the cast may round or truncate.
• GCD(0, 0) returns 0 by convention. Some mathematical texts leave this undefined; be explicit if your application treats zero inputs specially.
• For BIGINT inputs near the signed-minimum boundary, GCD(minimum, _) may overflow during the intermediate ABS step. Validate inputs upstream if they can reach the boundary.
• GCD is commutative (GCD(a, b) = GCD(b, a)) and associative via GCD(a, GCD(b, c)). Extend to more than two arguments with a reduce/fold pattern.
• For very large INT values, consider computing GCD in application code rather than SQL to take advantage of optimized bignum libraries.

See Also

• lcm
• div
• mod
• factorial