Common Factor Calculator

Find common factors and the Greatest Common Factor (GCF) of two or more numbers with detailed step-by-step solutions using multiple methods.

Enter Numbers

Numbers (separated by commas or spaces)

• Enter at least 2 positive integers

• Separate numbers with commas or spaces

• Example: 12, 18, 24

Results

Enter at least 2 numbers to find common factors

Methods to Find Common Factors

1. Listing Method

• List all factors of each number

• Find factors that appear in all lists

• The largest common factor is the GCF

• Good for smaller numbers

2. Prime Factorization

• Find prime factors of each number

• Take lowest powers of common primes

• Multiply to get GCF

• Efficient for larger numbers

3. Euclidean Algorithm

• For two numbers: GCD(a,b) = GCD(b, a mod b)

• Repeat until remainder is 0

• Very efficient for large numbers

• Extend to multiple numbers

4. Division Method

• Divide all numbers by small primes

• Continue until no common factors

• Multiply all common divisors

• Visual and systematic approach

Examples

Example 1: GCF of 12 and 18

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

GCF = 6

Example 2: GCF of 24, 36, and 48

24 = 2³ × 3

36 = 2² × 3²

48 = 2⁴ × 3

GCF = 2² × 3 = 12

Applications

Fraction Simplification

Use GCF to reduce fractions to lowest terms by dividing both numerator and denominator by their GCF.

Problem Solving

Solve problems involving equal groups, arrangements, and finding the largest possible size of equal parts.

Ratios and Proportions

Simplify ratios by dividing all terms by their GCF to get the simplest form of the ratio.

Number Theory

Foundation for understanding divisibility, modular arithmetic, and various mathematical proofs.

Frequently Asked Questions

Common factors are positive integers that divide two or more numbers evenly (with no remainder). For example, the common factors of 12 and 18 are 1, 2, 3, and 6.