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.
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