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Dernière mise à jour : 31 juillet 2026

GCF Calculator (Greatest Common Factor)

Dharmendra Singh - Creator

Créateurs

Dharmendra Singh

RĂ©viseurs

Balram Rajput
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Formule

List factors of a and b, intersect lists, then gcf = max(common factors)

OĂą :

  • a=First Positive Integer
  • b=Second Positive Integer
Greatest Common FactorA Venn diagram of the factors of 12 and 18 overlapping at 1, 2, 3, and 6, with 6 as the greatest common factor.12: 1,2,3,4,6,1218: 1,2,3,6,9,181, 2, 3, 6GCF = 6
The greatest common factor is the largest number that divides both numbers evenly.

Exemples résolus

Typical integers

Find common factors of 24 and 36.

  1. 1Factors of 24: 1,2,3,4,6,8,12,24
  2. 2Factors of 36: 1,2,3,4,6,9,12,18,36
  3. 3Intersection gives gcf 12
RĂ©ponse Finale: gcf=12, commonFactors=1, 2, 3, 4, 6, 12

Co-prime numbers

Find common factors of 14 and 25.

  1. 1List factor sets
  2. 2Only 1 appears in both
  3. 3Greatest common factor is 1
RĂ©ponse Finale: gcf=1, commonFactors=1

One divides another

Find common factors of 18 and 54.

  1. 1Every factor of 18 is also factor of 54
  2. 2Common factors end at 18
  3. 3So GCF is 18
RĂ©ponse Finale: gcf=18, commonFactors=1, 2, 3, 6, 9, 18

Introduction

GCF is the largest shared factor of two integers and is useful for reduction, grouping, and divisibility analysis.

Formula and Method

GCF Calculator (Greatest Common Factor) applies List factors of a and b, intersect lists, then gcf = max(common factors) and returns deterministic outputs from validated inputs.

  • Validate each required input

  • Apply the stated formula

  • Round numeric outputs where needed

  • Return safe defaults when validation fails

Input Fields

Use these keys exactly as defined in calculation.ts.

  1. 1

    a: First Positive Integer

  2. 2

    b: Second Positive Integer

Output Fields

These values map directly to calculation.ts return keys.

  1. 1

    gcf: Largest shared factor

  2. 2

    commonFactors: Comma-separated list of shared factors

Validation Rules

Both inputs must be positive integers.

  • Finite numeric values are required

  • Domain restrictions are enforced before solving

  • Invalid input returns default-safe outputs

  • Check examples to confirm expected behavior

How to Use This Calculator

Enter inputs, run the calculation, and read the primary output first.

  • Enter all required values

  • Click calculate

  • Review primary output first

  • Use supporting outputs for interpretation

Practical Uses

This calculator is useful for study, verification, and fast applied math checks.

  • Simplifying fractions

  • Factoring polynomials

  • Grouping objects evenly

  • Teaching factorization

FAQ

What does the GCF Calculator (Greatest Common Factor) compute?

It computes Greatest Common Factor and supporting outputs from your inputs.

Which inputs are required?

Required inputs are: First Positive Integer, Second Positive Integer.

How are invalid inputs handled?

When validation fails, the calculator returns safe default values and does not attempt invalid math.

Are results rounded?

Yes. Numeric outputs are rounded inside calculation.ts (typically to 6 decimal places).

Can I use negative or decimal values?

Only positive integers are accepted.

How should I verify my answer?

Use the worked examples and compare each output key with your manual steps.

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