Factor Calculator

Find all factors and prime factors of any number

Enter a Number

Enter any positive integer to find its factors

About Factors

🔢 What are Factors?

Factors are numbers that divide evenly into another number without leaving a remainder.

🌟 Prime Numbers

A prime number has exactly two factors: 1 and itself.

🔷 Composite Numbers

A composite number has more than two factors.

⚡ Prime Factorization

Breaking down a number into its prime number factors.

Examples

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About Factor Calculator

Our Factor Calculator helps you find all factors of any number, calculate prime factorization, and determine if a number is prime or composite. Perfect for students, teachers, and anyone working with numbers.

Features

  • Find all factors of any number up to 10 million
  • Calculate prime factorization with exponents
  • Check if a number is prime or composite
  • Display factor pairs that multiply to the number
  • Filter factors by type (prime, composite, even, odd)
  • Copy factors and factorization to clipboard
  • Visual color coding for prime and composite factors
  • Random number generator for exploration

How to Use

  1. Enter a positive integer (1 to 10,000,000)
  2. Click "Calculate Factors" or press Enter
  3. View all factors, prime factorization, and factor pairs
  4. Use filters to see specific types of factors
  5. Copy results to clipboard for easy sharing

Understanding Factors

Factors are whole numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder.

Prime vs Composite Numbers

  • Prime Numbers: Have exactly two factors (1 and itself). Examples: 2, 3, 5, 7, 11, 13
  • Composite Numbers: Have more than two factors. Examples: 4, 6, 8, 9, 10, 12
  • Special Case: The number 1 is neither prime nor composite

Prime Factorization

Prime factorization is the process of breaking down a composite number into its prime number factors. For example:

  • 12 = 2² × 3
  • 100 = 2² × 5²
  • 360 = 2³ × 3² × 5

Common Use Cases

  • Mathematics Education: Learning about factors, multiples, and divisibility
  • Simplifying Fractions: Finding common factors to reduce fractions
  • Number Theory: Studying properties of numbers
  • Problem Solving: Working on math problems and puzzles
  • Cryptography: Understanding prime numbers and factorization

Factor Properties

  • Every number has at least two factors: 1 and itself
  • Factors always come in pairs
  • The number of factors depends on the prime factorization
  • Perfect squares have an odd number of factors
  • Prime numbers have exactly 2 factors

Tips

  • Use the filter to focus on specific types of factors
  • Green badges indicate prime factors
  • Blue badges indicate composite factors
  • Factor pairs show all multiplication combinations
  • Copy results to use in other applications