CalcLibrary

Prime Factorization Calculator

Find the prime factors of any number. See the complete prime factorization, check if a number is prime, and count total divisors.

Examples

360 = 2^3 x 3^2 x 5

Prime Factors
2, 3, 5
Factorization
360 = 2^3 x 3^2 x 5
Is Prime?
No
Total Divisors
24

This number has 24 total divisors.

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Examples

How It Works

Formula

n=p1a1×p2a2×⋯×pkakn = p_1^{a_1} \times p_2^{a_2} \times \cdots \times p_k^{a_k}

d(n)=(a1+1)(a2+1)⋯(ak+1)d(n) = (a_1 + 1)(a_2 + 1) \cdots (a_k + 1)

Variables

nn

The integer being factored (n ≥ 2)

pip_i

The i-th distinct prime factor of n

aia_i

The exponent of the i-th prime in the factorization

kk

Number of distinct prime factors

d(n)d(n)

Total number of positive divisors of n

The calculator uses trial division: it divides the number by each integer starting from 2, counting how many times each prime divides evenly. The process continues until the remaining quotient is 1.

Frequently Asked Questions

01What is prime factorization?
Prime factorization is the process of finding which prime numbers multiply together to give the original number. Every integer greater than 1 has a unique prime factorization.
02What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
03Why is prime factorization useful?
It is fundamental in mathematics — used for finding GCD and LCM, simplifying fractions, cryptography (RSA), and number theory.
04How are the total divisors calculated?
If n = p1^a1 x p2^a2 x ... then the number of divisors is (a1+1)(a2+1)... For example, 360 = 2^3 x 3^2 x 5^1 has (3+1)(2+1)(1+1) = 24 divisors.
05What is the largest number supported?
This calculator supports numbers up to about 1 trillion (999,999,999,999). Larger numbers may take longer to factor.

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