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.

No. The number 1 has only one positive factor, so it is neither prime nor composite.

Math Calculators

Prime Factorization Calculator

Break a whole number into its prime factors and exponent form.

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Whole number

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.

Examples

Factor a number

Input: 60

Output: 2 x 2 x 3 x 5

60 is broken down into the prime numbers that multiply to make it.

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.

Open a related tool to prepare your files or refine the finished result.