Math Calculators
Prime Factorization Calculator
Break a whole number into its prime factors and exponent form.
Free foreverRuns in your browserNo sign-up
Prime factorization
23x32x5
2 x 2 x 2 x 3 x 3 x 5
About the Prime Factorization Calculator
Prime factorization expresses a whole number as a product of prime numbers. For example, 360 equals 2 cubed times 3 squared times 5.
Every integer greater than 1 has one unique prime factorization apart from the order of its factors. This makes prime factors useful for calculating LCM, GCF and simplifying fractions.
The calculator shows compact exponent form and the fully expanded multiplication, making the result useful for both quick answers and step-by-step learning.
Key features
- Compact exponent form
- Fully expanded prime factors
- Safe whole-number validation
- Instant browser-based calculation
How to use
- 1Enter a whole number of 2 or more.
- 2Read its prime factors in exponent form.
- 3Use the expanded line when individual repeated factors are needed.
Frequently asked questions
- What is a prime number?
- A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.
- Does every number have a prime factorization?
- Every whole number greater than 1 has a unique prime factorization, apart from the order of factors.
- Is 1 a prime number?
- No. The number 1 has only one positive factor, so it is neither prime nor composite.