Factor Calculator
Find all factors, prime factors, and prime factorization of any positive integer instantly.
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What Are Factors?
Factors of a number n are all positive integers that divide n without a remainder. The prime factorization expresses n as a product of prime numbers. Example: 360 = 2³ × 3² × 5. The number of factors can be found from the prime factorization: (3+1)(2+1)(1+1) = 24 factors.
What is the Factor Calculator?
The Factor Calculator instantly breaks down any integer into its constituent factors. It lists every single number that can divide perfectly into the target number without leaving a remainder. It is incredibly useful for prime factorization and simplifying algebraic fractions.
How It Works (Algorithm)
The tool loops through every integer from 1 up to the square root of the target number. If it finds an integer that divides evenly, it records both the divisor and the quotient as a paired set of factors.
$$ x \pmod y = 0 \implies y \text{ is a factor of } x $$
The modulo operation proves divisibility with zero remainder.
How to Use It
Enter the whole number you want to analyze. Hit calculate, and the tool will output a comprehensive, comma-separated list of all its factors, and can determine if the number is mathematically Prime or Composite.