--- title: "gcd" slug: "dev-database-reference-sql-functions-numeric-gcd" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-gcd" --- > ## Documentation Index > Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt > Use this file to discover all available pages before exploring further. # gcd *Applies to VAST Cluster 5.5.* *[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric) › Arithmetic.* `gcd(a, b)` returns the greatest common divisor of two integers: the largest whole number that divides both without a remainder. The result is never negative. `greatest_common_divisor` is the same function. ## Syntax ``` gcd(a, b) greatest_common_divisor(a, b) ``` | Argument | Type | Description | | --- | --- | --- | | `a`, `b` | any integer type up to `BIGINT`, `UBIGINT` or `HUGEINT` | The two integers. `DECIMAL` and floating-point values aren't accepted, even when they hold a whole number. | **Returns:** `BIGINT`, for every integer type up to `BIGINT`: `gcd(12::TINYINT, 18::TINYINT)` is a `BIGINT`. `UBIGINT` and `HUGEINT` arguments give a `HUGEINT`, which the ADBC driver returns as a `DECIMAL(38,0)` and Python prints as a `Decimal`. **Aliases:** `greatest_common_divisor`. ## Set up the examples The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_numeric_gcd`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see. This block connects, defines the `run()` and `plan()` helpers, and creates a table of three fractions, each a numerator (`BIGINT`) and a denominator (`INTEGER`). The second numerator is negative, the third is 0, and the last row has no values: ``` import os import re import adbc_driver_manager import adbc_driver_manager.dbapi as dbapi import adbc_driver_vastdb BUCKET = os.environ["VASTDB_BUCKET"] SCHEMA = f'"{BUCKET}/docs_sql_fn_numeric_gcd"' conn = dbapi.connect( driver=adbc_driver_vastdb.get_driver_path(), db_kwargs={ "vast.db.endpoint": os.environ["QE_ENDPOINT"], "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"], "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"], }, autocommit=True, ) def server_message(e): """The server's message in a driver error, without the request ID or the echoed statement.""" text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e)) found = (re.search(r'message: "(.*?)", request_id', text, re.S) or re.search(r"description: (.*)\)", text, re.S)) message = found.group(1) if found else text.strip().splitlines()[-1] message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S) message = re.split(r"\\n|\n", message)[0].replace('\\"', '"') return message.replace(BUCKET, "") def run(sql): """Run one statement. Print the rows it returns, or the error.""" try: with conn.cursor() as cur: cur.execute(sql) rows = cur.fetchall() if cur.description else [] except (adbc_driver_manager.Error, OSError) as e: print(f"{type(e).__name__}: {server_message(e)}") else: print(rows) def plan(sql): """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert.""" with conn.cursor() as cur: cur.execute("EXPLAIN " + sql) steps = cur.fetchall()[0][1] print("\n".join(line for line in steps.splitlines() if "Rows" not in line)) TABLE = f"{SCHEMA}.fractions" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, num BIGINT, den INTEGER)") run(f"INSERT INTO {TABLE} VALUES " "(1, 12, 18), " "(2, -42, 56), " "(3, 0, 5), " "(4, NULL, NULL)") ``` ``` [] [] [(4,)] ``` ## What it does `gcd(a, b)` is the largest whole number that divides both `a` and `b`: `gcd(12, 18)` is 6. - **Signs don't matter.** The result is the same for `a` and `-a`, and it's never negative: `gcd(-12, 18)`, `gcd(12, -18)` and `gcd(-12, -18)` are all 6. - **0 is divisible by everything,** so `gcd(0, 5)` and `gcd(5, 0)` are 5, and `gcd(0, 0)` is 0. - **Two arguments only.** For three or more values, nest the calls: `gcd(gcd(a, b), c)`. - **A numeric string is converted:** `gcd('12', 6)` is 6. A string that isn't a number fails with `Could not convert string 'abc' to INT64`. A common use is reducing a fraction: dividing the numerator and the denominator by their `gcd` gives the same fraction in lowest terms, as in the first example below. ## NULLs and edge cases | Input | Result | | --- | --- | | `gcd(NULL, 6)`, `gcd(6, NULL)` | `NULL` | | `gcd(12, 18)`, `greatest_common_divisor(12, 18)` | `6`, `6` | | `gcd(-12, 18)`, `gcd(12, -18)`, `gcd(-12, -18)` | `6`, `6`, `6` | | `gcd(0, 0)`, `gcd(0, 5)`, `gcd(5, 0)` | `0`, `5`, `5` | | `typeof(gcd(12::TINYINT, 18::TINYINT))` | `BIGINT` | | `gcd(18446744073709551615::UBIGINT, 5)` | `Decimal('5')`, a `HUGEINT` | | `gcd('12', 6)` | `6` | | The smallest `BIGINT`, -9223372036854775808, and 0 | Error: `Type INT128 with value 9223372036854775808 can't be cast because the value is out of range for the destination type INT64` | | `gcd(12.0, 18)` (a `DECIMAL`) | Error: `No function matches the given name and argument types 'gcd(DECIMAL(3,1), INTEGER_LITERAL)'` | | `gcd(1, 2, 3)` | Error: `No function matches the given name and argument types` | | A `DOUBLE`, date, boolean, `BLOB` or list | Error: `No function matches the given name and argument types` | The same cases, as the cluster returns them. They use the table and helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-gcd#set-up-the-examples): ``` run("SELECT gcd(NULL, 6), gcd(6, NULL), gcd(12, 18), greatest_common_divisor(12, 18)") run("SELECT gcd(-12, 18), gcd(12, -18), gcd(-12, -18), gcd(0, 0), gcd(0, 5), gcd(5, 0)") run("SELECT typeof(gcd(12::TINYINT, 18::TINYINT)), gcd(18446744073709551615::UBIGINT, 5), gcd('12', 6)") run("SELECT gcd(-9223372036854775808::BIGINT, 0)") run("SELECT gcd(12.0, 18)") run("SELECT gcd(1, 2, 3)") run("SELECT gcd(1.5::DOUBLE, 6)") ``` ``` [(None, None, 6, 6)] [(6, 6, 6, 0, 5, 5)] [('BIGINT', Decimal('5'), 6)] OSError: Type INT128 with value 9223372036854775808 can't be cast because the value is out of range for the destination type INT64 InternalError: Binder Error: No function matches the given name and argument types 'gcd(DECIMAL(3,1), INTEGER_LITERAL)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'gcd(INTEGER_LITERAL, INTEGER_LITERAL, INTEGER_LITERAL)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'gcd(DOUBLE, INTEGER_LITERAL)'. You might need to add explicit type casts. ``` ## Examples Each fraction in lowest terms: the numerator and the denominator divided by their `gcd`. The fraction 0/5 reduces to 0/1: ``` run(f"SELECT id, num, den, gcd(num, den), num // gcd(num, den), den // gcd(num, den) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 12, 18, 6, 2, 3), (2, -42, 56, 14, -3, 4), (3, 0, 5, 5, 0, 1), (4, None, None, None, None, None)] ``` The same with `greatest_common_divisor`, and the greatest common divisor of three values, nested: ``` run(f"SELECT id, greatest_common_divisor(num, den), gcd(gcd(num, den), 4) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 6, 2), (2, 14, 2), (3, 5, 1), (4, None, None)] ``` Keep only the fractions that are already in lowest terms: ``` run(f"SELECT id, num, den FROM {TABLE} WHERE gcd(num, den) = 1 ORDER BY id LIMIT 10") ``` ``` [] ``` ## How it runs in VAST The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). VAST DataBase can evaluate a comparison of a column with a constant, but not a function of a column, so `gcd()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the columns and the Query Engine computes `gcd()` for each row it returns. - **In `WHERE`,** the scan sends the columns for every row, and a `FILTER` step in the Query Engine computes `gcd()` and keeps the rows that match. No rows are skipped in storage. The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE gcd(num, den) = 1") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #2 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (gcd(num, CAST(den AS │ │ BIGINT)) = 1) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ num │ │ den │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Store the result if you filter on it often.** Compute `gcd()` when you write the rows and keep it in its own column, or store the fractions already reduced: a comparison of a column with a constant, such as `den = 3`, is pushed down to VAST DataBase. The plan for it has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE den = 3") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Combine it with a pushed-down condition.** In `id > 100 AND gcd(num, den) = 1`, `id > 100` is still evaluated in VAST DataBase, so `gcd()` runs only on the rows that pass it. ## Limitations and errors - **Integers only.** `DECIMAL`, `DOUBLE` and `FLOAT` values fail with `No function matches the given name and argument types`, even `12.0`. Cast them first: `gcd(CAST(x AS BIGINT), 18)`. - **Two arguments only.** `gcd(1, 2, 3)` fails with `No function matches the given name and argument types`. Nest the calls. - **The smallest `BIGINT` fails.** `gcd(-9223372036854775808::BIGINT, 0)` stops the query with `Type INT128 with value 9223372036854775808 can't be cast because the value is out of range for the destination type INT64`. `gcd(-9223372036854775808::BIGINT, -1)` fails the same way, although its result, 1, would fit. Cast to `HUGEINT` first, as in the block below. - **`UHUGEINT` isn't accepted** and fails with `No function matches the given name and argument types`. ``` run("SELECT gcd(CAST(12.0 AS BIGINT), 18), gcd(gcd(12, 18), 8)") run("SELECT gcd(CAST(-9223372036854775808 AS HUGEINT), 0)") ``` ``` [(6, 2)] [(Decimal('9223372036854775808'),)] ``` ## Similar functions | Function | Does | Result for `12` and `18` | | --- | --- | --- | | `gcd(a, b)`, `greatest_common_divisor(a, b)` | the largest number that divides both | `6` | | [lcm](/develop/docs/dev-database-reference-sql-functions-numeric-lcm), `least_common_multiple` | the smallest number both divide | `36` | | `a * b // gcd(a, b)` | the least common multiple, by hand | `36` | | [% (modulo)](/develop/docs/dev-database-reference-sql-functions-operators-modulo) | the remainder: `a % gcd(a, b)` is always 0 | `0` for `18 % 6` | ``` run("SELECT gcd(12, 18), greatest_common_divisor(12, 18), lcm(12, 18), least_common_multiple(12, 18), 12 * 18 // gcd(12, 18), 18 % gcd(12, 18)") ``` ``` [(6, 6, 36, 36, 36, 0)] ``` Clean up: ``` run(f"DROP TABLE IF EXISTS {TABLE}") run(f"DROP SCHEMA IF EXISTS {SCHEMA}") conn.close() ``` ``` [] [] ``` ## See also - [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric#arithmetic): all the arithmetic functions. - [lcm](/develop/docs/dev-database-reference-sql-functions-numeric-lcm), [factorial](/develop/docs/dev-database-reference-sql-functions-numeric-factorial) and [% (modulo)](/develop/docs/dev-database-reference-sql-functions-operators-modulo). - [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns). - [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.