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mathematics Verified Precision Tool

Prime Factorization Calculator

Decompose any integer into its unique prime factor product tree.

Calculation Solution
Prime Factors: 2 × 2 × 5 × 5
Product: 100

Mathematical Formula

N = p1^a * p2^b * ... * pk^m

Overview & Explanation

The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either prime or can be uniquely represented as a product of prime numbers.

How It Works

  • Divide the number by the smallest prime factor (2).
  • Continue dividing by primes (3, 5, 7...) until the quotient is 1.

Practical Applications

  • Simplifying radicals and roots.
  • Solving encryption algorithms.

Worked Example: Prime Factors of 360

Find prime factors.

1

Factorize iteratively

360 / 2 = 180, / 2 = 90, / 2 = 45, / 3 = 15, / 3 = 5, / 5 = 1

= 2^3 * 3^2 * 5

Frequently Asked Questions

What is prime factorization?
Prime factorization breaks down a composite number into a product of prime numbers.