Prime Factorization Visualizer
Prime Factorization Visualizer computes the prime factorization of a positive integer and visualizes the frequency of each prime factor.
Prime Factorization Overview
Prime factorization expresses a positive integer as a product of prime numbers raised to certain powers. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
Formula: \\( n = p_1^{e_1} \cdot p_2^{e_2} \cdot \dots \cdot p_k^{e_k} \\)
Where:
- \\( n \\): Input number (positive integer)
- \\( p_i \\): Prime factors
- \\( e_i \\): Exponents (multiplicities of each prime factor)
Example Calculations
Example 1: Number = 100
Prime Factorization: \\( 100 = 2^2 \cdot 5^2 \\)
Prime Factors: \\( \{2, 5\} \\), Multiplicities: \\( \{2, 2\} \\)
Example 2: Number = 60
Prime Factorization: \\( 60 = 2^2 \cdot 3^1 \cdot 5^1 \\)
Prime Factors: \\( \{2, 3, 5\} \\), Multiplicities: \\( \{2, 1, 1\} \\)
Example 3: Number = 17
Prime Factorization: \\( 17 = 17^1 \\)
Prime Factors: \\( \{17\} \\), Multiplicities: \\( \{1\} \\)
Example 4: Number = 1
Prime Factorization: \\( 1 \\) (no prime factors)