Factor Calculator

Find all factors, prime factors, and factor pairs of any number

Numbers up to 10,000,000 supported

What is a Factor?

A factor of a number is an integer that divides exactly into that number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Types of Factors

Prime Factors

Factors that are prime numbers (divisible only by 1 and themselves).

12 = 2 × 2 × 3

Factor Pairs

Two numbers that multiply together to make the original number.

12: (1,12), (2,6), (3,4)

Calculation Methods

  • Trial Division: Test divisibility by all integers up to √n
  • Prime Factorization: Break down into prime components first
  • Efficient Algorithms: For very large numbers (not implemented here)

Practical Applications

Simplifying fractions
Cryptography
Number theory problems
Finding common denominators

About the Factor Calculator

Our Factor Calculator is a comprehensive online tool that helps you find all the factors of any positive integer. Whether you're a student learning number theory, a teacher preparing math lessons, or just curious about number properties, this calculator provides instant results with detailed information about your number.

Key Features

Complete Factor Analysis

Get all factors, prime factors, factor pairs, and prime factorization in one place.

Visual Prime Factorization

See the prime factorization displayed as both an equation and a factor tree.

Educational Resources

Learn about factors with our explanations and practical examples.

Common Factor Examples

Number Factors Prime Factors Factor Pairs
12 1, 2, 3, 4, 6, 12 2² × 3 (1,12), (2,6), (3,4)
17 1, 17 17 (1,17)
24 1, 2, 3, 4, 6, 8, 12, 24 2³ × 3 (1,24), (2,12), (3,8), (4,6)

Frequently Asked Questions

Factors are all integers that divide evenly into a number. Prime factors are a subset of these - only the factors that are prime numbers. Every number can be expressed as a unique product of its prime factors.

Example for 36:
Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
Prime Factors: 2, 3 (since 36 = 2 × 2 × 3 × 3)

The most efficient method is to check divisibility up to the square root of the number:

  1. Start with 1 (which is a factor of every number)
  2. Check divisibility by integers up to √n
  3. For each factor found, its pair is n divided by the factor
  4. For prime factorization, divide by primes until you reach 1

Our calculator implements these methods to provide instant results.

Factors are fundamental in many areas of mathematics including:

  • Fractions: Simplifying and finding common denominators
  • Algebra: Factoring polynomials
  • Number Theory: Studying properties of integers
  • Cryptography: RSA encryption relies on prime factorization
  • Real-world applications: Dividing items into equal groups, scheduling repeating events