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
Factor 360
360 = 2^3 x 3^2 x 5
- Number
- 360
Prime Factors
2, 3, 5
Factorization
360 = 2^3 x 3^2 x 5
Is Prime?
No
Total Divisors
24
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How It Works
Formula
Variables, symbols and units
- The integer being factored (n ≥ 2)
- The i-th distinct prime factor of n
- The exponent of the i-th prime in the factorization
- Number of distinct prime factors
- Total number of positive divisors of n
Calculation method explained
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.
Examples
Factor 360360 → 2, 3, 5
360 = 2^3 x 3^2 x 5
- Number
- 360
- Prime Factors
- 2, 3, 5
Check a prime97 → 97
97 is a prime number
- Number
- 97
- Prime Factors
- 97
Large composite1,024 → 2
1024 = 2^10
- Number
- 1,024
- Prime Factors
- 2
Frequently Asked Questions
What 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.
What 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.
Why is prime factorization useful?
It is fundamental in mathematics — used for finding GCD and LCM, simplifying fractions, cryptography (RSA), and number theory.
How 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.
What 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.