Prime Factorization Calculator

Find prime factors and complete prime factorization of any positive integer greater than 1. Detailed step-by-step solutions shown with successive division method.

What is Prime Factorization?

Prime numbers are positive integers greater than 1 that have exactly two distinct positive divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, ...

Prime factorization is the process of expressing a composite number as the product of its prime factors. The Unique Prime Factorization Theorem states that every integer greater than 1 is either prime or can be represented uniquely as a product of prime numbers (ignoring order).

For example, the prime factorization of 24 is \( 2 \times 2 \times 2 \times 3 = 2^3 \times 3 \).

Example: Prime Factorization of 120

Successive divisions by prime numbers (2, 3, 5, 7, ...):

\( 120 \div \color{red}{2} = \color{black} {60} \)
\( 60 \div \color{red}{2} = \color{black} 30 \)
\( 30 \div \color{red}{2} = \color{black} 15 \)
\( 15 \div \color{red}{3} = \color{black} 5 \)
\( 5 \div \color{red}{5} = \color{black} 1 \)

Prime factorization: \( 120 = 2 \times 2 \times 2 \times 3 \times 5 = 2^3 \times 3 \times 5 \)

Prime Factorization Calculator

Enter a positive integer greater than 1 to get its prime factorization with detailed steps.
Enter integers, decimals will be truncated to integer part.
Enter a number greater than 1 and click "Factorize"
Step-by-step solution will appear here after calculation.

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