Prime Factorization Calculator interactive tool
Enter an integer
Prime factorization
Prime factorization of 360:
2^3 × 3^2 × 5
A prime factorization expresses a composite number as a product of prime numbers. Each prime factor may appear more than once, indicated by the exponent.
What Is Prime Factorization?
A prime factorization calculator breaks a whole number down into a product of prime numbers, like 360 = 2³ × 3² × 5. This is one of the most important building blocks in arithmetic and number theory.
Why Prime Factors Matter
- They are used to find greatest common divisors (GCD) and least common multiples (LCM).
- They help simplify fractions to lowest terms.
- They are essential in more advanced topics like cryptography and modular arithmetic.
Manually factoring large numbers can be tedious. This prime factorization tool automates the trial division process so you can quickly see the prime powers behind any composite integer.
How To Use the Prime Factorization Calculator
- Enter an integer greater than 1 into the input field.
- Press Enter or simply stop typing; the prime factorization calculator runs automatically in your browser.
- Review the prime factorization written as a product of prime numbers using exponents where appropriate.
- Use the result to check homework, find GCD/LCM, or better understand number theory exercises.
- Use the Example button to see a fully factored sample like 360, or Reset to clear the input.