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Every whole number greater than 1 can be broken down into a unique product of prime numbers — its prime factorization.
This calculator finds the prime factorization of any number by repeated division, showing the full working.
How it works
Enter a whole number. The calculator repeatedly divides by the smallest prime that divides it evenly, continuing on the result until only 1 remains, then lists the primes found — grouping repeated factors with exponents.
- Enter number.
- Click Calculate to see your results.
Examples
Factoring 60
60 = 2 × 2 × 3 × 5, or written with exponents, 2² × 3 × 5.
A prime number
97 has no factors other than 1 and itself, so its prime factorization is just 97.
Who should use it
- Checking number theory or algebra homework.
- Finding the building blocks needed to compute a GCD or LCM by hand.
Industry applications
- Mathematics education
- Computer science and cryptography fundamentals
Advantages
- Shows both the expanded factor list and the compact exponent notation.
- Handles prime numbers as a clear special case.
Limitations
- Very large numbers (in the billions or higher) aren't supported, since trial division becomes impractical at that scale.
Common mistakes to avoid
- Forgetting that 1 and the number itself aren't counted as "factors" in a prime factorization — only prime numbers count.
- Stopping the division process before reaching 1, leaving a composite number in the factor list.
Best practices
- When comparing two numbers' factorizations (for GCD or LCM), write both using the same set of prime bases, even if one has a zero exponent for a given prime.
Tips
- To manually check a factorization, multiply all the listed prime factors back together — the result should equal the original number.