Prime Factorization Calculator
Instantly find the prime factorization of any positive integer. Visualize the decomposition with a factor tree and see the result in exponent form.
Prime Factorization Calculator
Instantly find the prime factorization of any positive integer. Visualize the decomposition with a factor tree and see the result in exponent form.
What is Prime Factorization?
Prime factorization is the process of breaking down a composite number into the prime numbers that, when multiplied together, equal the original number. Think of prime numbers as the 'building blocks' of all integers. For example, 12 can be broken down into 2 × 2 × 3. According to the Fundamental Theorem of Arithmetic, every integer greater than 1 has a unique prime factorization.
Examples
Key Concepts
- •Prime Number: A number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5, 7).
- •Composite Number: A number that has more than two factors.
- •Factor Tree: A visual tool used to break down a number step-by-step until only prime numbers remain.
- •Exponent Notation: A concise way to write repeated prime factors (e.g., 2 × 2 × 2 = 2^3).
Real-World Applications
- •Cryptography: Large prime numbers are the foundation of modern encryption (like RSA) that keeps internet data secure.
- •Mathematics: Essential for finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM).
- •Fractions: Used to simplify fractions to their lowest terms.
- •Computing: Helps in algorithms for hashing and data security.
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Least Common Multiple Calculator
Calculate the Least Common Multiple (LCM) of two or more numbers with step-by-step solutions.