How does the factorization algorithm work for large numbers?

The tool uses trial division up to √n combined with Pollard's rho algorithm for large numbers. This handles most 15-digit numbers within milliseconds in the browser.

What is a perfect number?

A perfect number equals the sum of its proper divisors (excluding itself). The first perfect numbers are 6 (1+2+3), 28 (1+2+4+7+14), and 496. Numbers whose divisor sum exceeds them are abundant; less are deficient.

What is the difference between GCD and LCM?

GCD (Greatest Common Divisor) is the largest number that divides both inputs exactly. LCM (Least Common Multiple) is the smallest number divisible by both inputs. GCD × LCM = product of the two numbers.

Why is 1 neither prime nor composite?

By definition, a prime must have exactly two distinct positive divisors (1 and itself). The number 1 has only one divisor, so it is classified as neither prime nor composite — it is a unit.

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Prime Factorization Calculator

Factorize numbers up to 10¹⁵ with SVG factor trees

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关于此工具

Enter any integer up to 1,000,000,000,000,000 (10¹⁵) to see its complete prime factorization with exponents. An interactive SVG factor tree visualises the decomposition step by step. A two-number section lets you compute GCD (Greatest Common Divisor) and LCM (Least Common Multiple) instantly. The tool also classifies each number as prime, perfect, abundant, or deficient.

使用方法

1 Enter an integer up to 10¹⁵ in the input field and click Factorize.
2 View the prime factorization expressed with exponents (e.g. 2³ × 3 × 7²).
3 Explore the SVG factor tree to see how the number breaks down step by step.
4 Enter a second number in the GCD/LCM section to compute their GCD and LCM.

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