About

Every integer greater than 1 is either a prime number itself or can be represented as the product of prime numbers. This is known as the Fundamental Theorem of Arithmetic. Prime factorization breaks a composite number down into its atomic elements (e.g., 12 becomes 2 × 2 × 3).

This tool is designed for students and educators. It not only provides the standard Canonical Form (using exponents like 2³) but also generates a textual "Step-by-Step Factor Tree" to visualize the division process. It handles large integers efficiently and checks for primality instantly.

Formulas

To find the prime factorization of n, we repeatedly divide by the smallest prime factor p:

n = p₁^a × p₂^b × ...

We check divisibility starting from 2, then 3, then 5, and so on up to √n.

Reference Data

Number	Prime Factors	Canonical Form	Is Prime?
12	2, 2, 3	2² × 3	No
31	31	31	Yes
100	2, 2, 5, 5	2² × 5²	No
1024	2 (10 times)	2¹⁰	No
5040	2, 2, 2, 2, 3, 3, 5, 7	2⁴ × 3² × 5 × 7	No

Frequently Asked Questions

Canonical form is the standard way of writing prime factors where primes are ordered from smallest to largest, and repeated factors are grouped into exponents (e.g., instead of 2 x 2 x 2, we write 2^3).

No, 1 is not considered a prime number because it has only one divisor (itself). A prime number must have exactly two distinct positive divisors: 1 and itself.

The tool uses an optimized Trial Division algorithm. For extremely large numbers (15+ digits), calculation time may increase, but it is generally instant for standard schoolwork problems.