Find prime factors of any number with step-by-step solutions
Prime factorization is the process of decomposing a composite number into a product of its prime factors. Every composite number can be expressed as a unique product of prime numbers.
Prime Factorization Result
Step-by-Step Calculation
Prime Factorization Algorithm
This calculator uses the Trial Division Method to find prime factors:
Start with the smallest prime number (2)
Divide the number by this prime as many times as possible
Move to the next prime number and repeat
Continue until the quotient becomes 1
Examples
Factorization of 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Prime Factors: 2 × 2 × 3 × 5 = 2² × 3 × 5
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Prime Factors: 2 × 2 × 3 × 5 = 2² × 3 × 5
Factorization of 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
Prime Factors: 2 × 2 × 3 × 7 = 2² × 3 × 7
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
Prime Factors: 2 × 2 × 3 × 7 = 2² × 3 × 7
Mathematical Background
Prime Numbers: Natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
Fundamental Theorem of Arithmetic: Every integer greater than 1 is either prime itself or can be represented as a unique product of prime numbers.
Real-World Applications
Cryptography: RSA encryption relies on prime factorization
Mathematics: Finding GCD/LCM and simplifying fractions
Computer Science: Algorithm design and complexity analysis
Number Theory: Solving Diophantine equations
Leave a Reply