🔢 Common Factor Calculator
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What Are Common Factors?
A common factor (or common divisor) is a number that divides two or more integers exactly without leaving a remainder. For example, the numbers 12 and 18 share the factors 1, 2, 3, and 6 – so these are their common factors.
The largest of these common factors is called the Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD). Knowing the GCF is extremely useful for simplifying fractions, solving ratio problems, and understanding number relationships.
How to Find Common Factors
- Prime factorization: Break each number down into its prime factors.
- Identify shared primes: Look for prime factors that appear in both numbers.
- Multiply the smallest powers: For each shared prime, take the lower exponent and multiply them – this gives the GCF.
- List all divisors: Every divisor of the GCF is a common factor of the original numbers.
💡 Example with 24 and 36
24 = 23 × 3
36 = 22 × 32
Shared primes: 2 and 3 → GCF = 22 × 3 = 12
Divisors of 12: 1, 2, 3, 4, 6, 12 – these are the common factors of 24 and 36.
Use the calculator above to instantly see the prime factorization, greatest common factor, and the complete list of common factors for any two positive integers. Perfect for homework, teaching, or quick math checks!
