Prime Factorization Calculator

Break any integer into its prime factors.

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Enter any integer from 2 to 999,999,999

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PRIME

COMPOSITE

Prime Factors

Standard Notation

Smallest Prime

Largest Prime

Total Number of Divisors

Factor Tree

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Enter a number above and tap Factorize to see prime factors and divisors.

Step-by-step Solution

What is Prime Factorization?

Prime factorization is the process of breaking down a composite number into its prime number factors. Every integer greater than 1 is either prime or can be expressed as a unique product of primes.

Notation

N = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ

Where p₁, p₂, ..., pₖ are prime numbers and a₁, a₂, ..., aₖ are their respective exponents.

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Pro Tips

Prime factorization is unique for every number (Fundamental Theorem of Arithmetic).

Use prime factorization to find GCF and LCM of numbers easily.

The total number of divisors can be calculated using the formula: (a₁+1)(a₂+1)...(aₖ+1).

For large numbers, only test divisibility up to √n to check primality.