GCF Calculator

Find the greatest common factor of two whole numbers using the Euclidean algorithm.

GCF Calculator

Find the greatest common factor of two whole numbers using the Euclidean algorithm.

First number

Second number

Enter values above and click Calculate — results will appear here with the formula explained.

Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF

How does this work?

The Euclidean algorithm finds it without factoring: keep replacing the pair (a, b) with (b, a mod b). The remainders shrink quickly, and the last non-zero remainder is the answer — remarkably efficient even for enormous numbers.

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What is GCF?

The greatest common factor (also called GCD or HCF) is the largest whole number that divides both inputs without a remainder. It is what you divide by to reduce a fraction: 48/36 reduces to 4/3 because GCF = 12. Formula: Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF

Quick Answer

GCF Calculator computes find the greatest common factor of two whole numbers using the euclidean algorithm. Formula: Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0. Example: GCF(48, 36): 48 mod 36 = 12, then 36.

What it does: Find the greatest common factor of two whole numbers using the Euclidean algorithm.
Formula: Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF
Inputs: First number · Second number
Example: GCF(48, 36): 48 mod 36 = 12, then 36 mod 12 = 0, so the GCF is 12.

Calculator Inputs at a Glance

Field	What to enter
First number	e.g. 48
Second number	e.g. 36

All fields use the exact formulas shown below — results include step-by-step breakdowns you can verify by hand.

How to Use This Calculator

1Enter two whole numbers into the fields to compute their greatest common divisor.
2The greatest common factor appears instantly.
3Each input divided by the GCF is shown, which is exactly what you need to reduce a fraction.

Formula Used

Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF

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Worked Example

GCF(48, 36): 48 mod 36 = 12, then 36 mod 12 = 0, so the GCF is 12. Reducing 48/36 by 12 gives 4/3.

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Frequently Asked Questions

QWhat is the fastest way to find the GCF?

The Euclidean algorithm — divide, take the remainder, repeat. It avoids listing factors entirely and works instantly even on huge numbers.

QAre GCF and GCD the same thing?

Yes — greatest common factor, greatest common divisor and highest common factor are three names for one concept.

QWhat is the GCF of consecutive numbers?

Always 1. Consecutive integers share no factor greater than 1, so fractions like 997/998 are already in lowest terms.

What is GCF?

Quick Answer

What it does: Find the greatest common factor of two whole numbers using the Euclidean algorithm.

Formula: Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF

Inputs: First number · Second number

Example: GCF(48, 36): 48 mod 36 = 12, then 36 mod 12 = 0, so the GCF is 12.

Field

What to enter

First number

e.g. 48

Second number

e.g. 36

Formula Used

Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF

Frequently Asked Questions

QWhat is the fastest way to find the GCF?

The Euclidean algorithm — divide, take the remainder, repeat. It avoids listing factors entirely and works instantly even on huge numbers.

QAre GCF and GCD the same thing?

Yes — greatest common factor, greatest common divisor and highest common factor are three names for one concept.

QWhat is the GCF of consecutive numbers?

Always 1. Consecutive integers share no factor greater than 1, so fractions like 997/998 are already in lowest terms.