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CalcivoTools

Prime Factorization Calculator : Factor Tree Decomposition & Exponential Form

The Calcivo Prime Factorization Calculator breaks down any composite number n ≥ 2 into its unique prime components. By the Fundamental Theorem of Arithmetic, every integer has a unique representation as a product of prime powers.

Interactive Calculator

100% Client-Side Engine
Canonical Prime Factorization (360)
2^3 × 3^2 × 5
Expanded Prime Product
2 × 2 × 2 × 3 × 3 × 5
Total Divisors Count d(n)
24 positive divisors
Factor Tree Decomposition Steps
Divide by 2: extracted 2^3, remaining = 45
Divide by 3: extracted 3^2, remaining = 5
Remaining factor is prime: 5

Step-by-Step Examples

Prime Factorization of 360

Decomposing 360 into prime powers.

Inputs: Number (n): 360
Result: 2³ × 3² × 5 (Total Divisors: 24)

360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.

How to Use This Tool

  1. Enter a positive composite integer (n ≥ 2).
  2. Click Calculate.
  3. Review canonical prime powers (e.g. 2³ × 3² × 5), expanded factor lists, and step-by-step division tree.

Frequently Asked Questions

Add 1 to each prime exponent and multiply them together: d(n) = (a₁ + 1)(a₂ + 1)...(a_k + 1). For 360 (2³ × 3² × 5¹): (3+1)(2+1)(1+1) = 4 × 3 × 2 = 24 divisors.

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