Professional Factor Calculator

Find all factors of a number, check if it's prime, and get prime factorization with step-by-step solutions and visualizations.

Calculator

Enter a positive integer (1 to 10,000,000,000)

Enter a positive integer to find all its factors, check if it's prime, and get prime factorization.

Complete User Guide

What is the Factor Calculator?

The Factor Calculator finds all factors of a given number, determines if it's prime, and provides prime factorization. Factors are numbers that divide evenly into the given number.

This calculator is useful for number theory, simplifying fractions, finding divisors, and understanding number properties.

How to Use This Calculator

  1. Enter a positive integer (1 to 10,000,000,000)
  2. Click 'Calculate Factors' to find all factors
  3. View the prime status (prime or composite)
  4. See all factors displayed as tags
  5. Review prime factorization and detailed results
  6. Use charts to visualize factor distribution
  7. Follow the step-by-step solution to understand the process

Understanding the Results

  • Prime Status: Indicates whether the number is prime (has exactly 2 factors) or composite (has more than 2 factors)
  • All Factors: Complete list of all numbers that divide evenly into the given number
  • Total Factors: Count of all factors including 1 and the number itself
  • Proper Factors: All factors except the number itself
  • Prime Factorization: Expression of the number as a product of prime numbers raised to their powers

Examples

Example 1: Prime Number

Number: 7

Is Prime? 是

Factors: 1, 7

Prime Factorization: 7

Example 2: Composite Number

Number: 24

Is Prime? 否

Factors: 1, 2, 3, 4, 6, 8, 12, 24

Prime Factorization: 2³ × 3

Example 3: Large Number

Number: 100

Is Prime? 否

Factors: 1, 2, 4, 5, 10, 20, 25, 50, 100

Prime Factorization: 2² × 5²

Key Concepts

Prime Number

A number greater than 1 that has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23.

Composite Number

A number greater than 1 that has more than two factors. Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16.

Prime Factorization

Every composite number can be expressed uniquely as a product of prime numbers. For example, 12 = 2² × 3, and 60 = 2² × 3 × 5.

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