GCD / HCF Calculator

How the GCD / HCF Calculator Works

The greatest common divisor (GCD) — also known as the highest common factor (HCF) — is the largest whole number that divides every one of your numbers exactly. This calculator accepts two or more positive whole numbers and returns the GCD plus the LCM for reference.

The Method

The tool uses the Euclidean algorithm, the classic and efficient way to find a GCD:

GCD(a, b) = GCD(b, a mod b), repeated until the remainder is 0.

You divide the larger number by the smaller, keep the remainder, then repeat with the smaller number and that remainder. When the remainder reaches 0, the last divisor is the GCD. For more than two numbers, the algorithm is applied pairwise across the list.

Worked Example

Find the GCD of 48 and 36:

Step	a	b	a mod b
1	48	36	12
2	36	12	0

When the remainder hits 0, the last divisor (12) is the answer. So the GCD of 48 and 36 is 12. Extending to a third number such as 60: GCD(12, 60) is still 12.

Why the GCD Matters

The GCD is one of the most useful tools in arithmetic:

• Simplifying fractions — divide the numerator and denominator by their GCD to reach lowest terms.
• Equal grouping — split items into the largest possible equal-sized groups.
• Ratios — reduce a ratio to its simplest form using the GCD.

Because the GCD and LCM are linked, this tool shows both so you can move between them easily.