Find GCD in JavaScript (Euclidean algorithm, BigInt, mathjs)

The greatest common divisor (GCD) of integers is the largest positive integer that divides each of them with remainder zero. (It is not a “denominator”—that word belongs to fractions.) For gcd javascript, javascript gcd, or greatest common divisor javascript searches, the usual implementation is Euclid’s algorithm: repeatedly replace (a, b) with (b, a % b) until b is zero. That shows up when simplifying fractions, aligning repeating cycles, and in small numeric utilities.

Tested on: Node.js v20.18.2. A short note after each snippet states the expected value; the mathjs example needs npm install mathjs and uses {run=false} in the in-page runner.

Quick reference

Use this table when you need a javascript gcd function for two numbers, a list, BigInt, or a quick variadic call via mathjs.

1. Recursive Euclidean javascript gcd

The recursive form matches the math definition directly: gcd(a, b) equals gcd(b, a % b) until b === 0, then return a. It is easy to read for js gcd tutorials; for very deep chains you may prefer iteration to avoid stack growth.

function gcd(a, b) {
  if (b === 0) {
    return a;
  }
  return gcd(b, a % b);
}

console.log(gcd(12, 18));

You should see 6.

2. Iterative form (often preferred for js gcd)

An iterative javascript gcd function uses a while loop and swaps (a, b) with (b, a % b) until b is zero—same mathematics as recursion, usually better for production when inputs can be large. Math.abs normalizes signs so gcd javascript behaves the usual way on negative literals.

function gcdIter(a, b) {
  a = Math.abs(a);
  b = Math.abs(b);
  while (b !== 0) {
    const t = b;
    b = a % b;
    a = t;
  }
  return a;
}

console.log(gcdIter(48, 18));
console.log(gcdIter(-12, 18));
console.log(gcdIter(0, 7));

Three lines: 6, 6 again after normalizing -12, and 7 for gcd(0, 7).

3. gcd in javascript for many numbers

GCD is associative: gcd(a, b, c) equals gcd(gcd(a, b), c), so you can fold any non-empty list with reduce once you have a solid two-argument gcd in javascript helper.

function gcdTwo(a, b) {
  a = Math.abs(a);
  b = Math.abs(b);
  while (b !== 0) {
    const t = b;
    b = a % b;
    a = t;
  }
  return a;
}

function gcdList(nums) {
  return nums.reduce((acc, n) => gcdTwo(acc, n));
}

console.log(gcdList([12, 18, 24]));

Folding pairwise over [12, 18, 24] yields 6.

4. gcd in js with BigInt

For integers larger than Number.MAX_SAFE_INTEGER, keep the whole javascript greatest common divisor calculation in BigInt: use 0n, %, and n literals end-to-end. Mixing BigInt with Number in one expression throws, so convert explicitly if you must bridge types.

function gcdBig(a, b) {
  a = a < 0n ? -a : a;
  b = b < 0n ? -b : b;
  while (b !== 0n) {
    const t = b;
    b = a % b;
    a = t;
  }
  return a;
}

console.log(gcdBig(120n, 84n));

You should see 12n.

5. Optional: mathjs for gcd js variadic calls

When a dependency is fine, mathjs exposes a variadic gcd so you can write gcd(12, 18, 24) without folding manually—useful for scripts and calculators, not for every bundle. Install with npm install mathjs, then require or import the function (mathjs gcd docs). The snippet is {run=false} because the public runner does not ship mathjs.

const { gcd } = require("mathjs");

console.log(gcd(12, 18, 24));

6

With mathjs installed locally (the article used mathjs@13 with CommonJS require), the log prints 6.

Summary

These patterns cover most javascript gcd needs in application code: a tiny Euclidean core, sign normalization, list folding, BigInt, and an optional mathjs shortcut.

• GCD is the largest shared divisor; Euclid’s algorithm uses repeated modulo until b === 0.
• Normalize negatives with Math.abs (or sign checks for BigInt).
• Fold reduce across an array for more than two operands; mathjs helps when you want variadic ergonomics.

References

Wikipedia and mathjs documentation for gcd javascript algorithms.

• Wikipedia: Greatest common divisor
• Wikipedia: Euclidean algorithm
• mathjs gcd