Factor any number into its prime factors

Break an integer into grouped prime powers whose product reconstructs the input.

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ToolPrime Factorization
Input
Output
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Preview

How it works

Candidate divisors are tried from 2 upward; each successful divisor is repeatedly removed, and remaining factors are grouped by exponent. Multiplying the displayed prime powers recovers the original integer.

  • Inputs begin at 2.
  • Trial division is exact but not a fast large-semiprime algorithm.

Worked example

Factorize 360
Find the prime factorization of 360
Input
											360
Output
												360 = 2^3 × 3^2 × 5

When to use this

Number theory expands integers, fraction reducers compare prime exponents, and cryptography exercises inspect small factor structure.

Edge cases

  • A prime returns itself with exponent one.
  • 72 becomes 2³ × 3² rather than a flat list.
  • Large semiprimes can make trial division slow.