Factor Calculator
Find all factors and prime factors of a number.
Number Input
Enter a positive integer from 1 to 1000
Factor Results
Total Factors
8
All Factors
1, 2, 3, 4, 6, 8, 12, 24
Prime Factorization
24 = 2^3 × 3
Factor Pairs:
(1, 24)(2, 12)(3, 8)(4, 6)
About This Calculator
The Factor Calculator helps you find all factors of a number, determine prime factors, and check if a number is prime. Factors are numbers that divide evenly into another number without leaving a remainder.
Enter any integer, and the calculator will list all its factors, show the prime factorization (expressing the number as a product of prime numbers), indicate whether the number is prime, and display factor pairs. This is useful for number theory, simplifying fractions, and mathematical analysis.
Formula & Calculation Method
Factor Concepts:
Factors:
Numbers that divide evenly into the given number
Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Prime Factors:
Prime numbers that multiply to give the number
Example: 12 = 2 × 2 × 3 = 2² × 3
Prime Number:
A number with exactly two factors: 1 and itself
Example: 7 is prime (factors: 1, 7)
Factorization involves finding all numbers that divide evenly into the given number. Prime factorization expresses a number as a product of prime numbers, which is unique for each number (fundamental theorem of arithmetic).
How to Use This Calculator
- Enter Number: Input the integer you want to factor.
- View Results: See all factors, prime factors, prime factorization, and factor pairs.
- Check Prime: See if the number is prime (has exactly 2 factors).
- Use Factors: Use factors to simplify fractions, find common denominators, or solve problems.
Frequently Asked Questions
What are factors?
Factors are numbers that divide evenly into another number without leaving a remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these divides 12 evenly.
What is prime factorization?
Prime factorization expresses a number as a product of prime numbers. For example, 12 = 2 × 2 × 3 = 2² × 3. Every composite number has a unique prime factorization (fundamental theorem of arithmetic).
What is a prime number?
A prime number is a number greater than 1 that has exactly two factors: 1 and itself. Examples include 2, 3, 5, 7, 11, 13, etc. Prime numbers cannot be factored further.
What are factor pairs?
Factor pairs are two numbers that multiply together to give the original number. For example, factor pairs of 12 are (1, 12), (2, 6), and (3, 4). Each pair multiplies to 12.
NumCalculators Editorial Team
Multi-disciplinary Expert Team
The NumCalculators Editorial Team consists of subject matter experts across various fields who review and verify the accuracy of our calculators. Each calculator undergoes rigorous testing and validation before publication.