Prime Factorization
Enter a whole number from 2 and see its prime factorization written as a product of prime powers. The result follows the usual school method: trial division by primes, then exponents for repeated factors. Useful alongside GCD/LCM work and for checking factor trees.
Whole number ≥ 2 (e.g. 360 for class practice).
Enter a whole number from 2 and see its prime factorization written as a product of prime powers. The result follows the usual school method: trial division by primes, then exponents for repeated factors. Useful alongside GCD/LCM work and for checking factor trees.
Every integer n > 1 can be written uniquely (up to order) as n = p1^a1 × p2^a2 × … × pk^ak where each pi is prime and each ai is a positive whole number.
360 ÷ 2 → 180 ÷ 2 → 90 ÷ 2 → 45, then 45 ÷ 3 → 15 ÷ 3 → 5, then 5 ÷ 5 → 1. So 360 = 2^3 × 3^2 × 5^1. The tool prints that compact form and how many distinct primes appear.
GCD finds the largest shared divisor of two numbers. This tool breaks one number into its prime building blocks. You often use prime factors first, then read off GCD and LCM by comparing exponents.
No. Prime factorization is defined for integers greater than 1. The tool asks for a whole number from 2 upward so the mathematics stays standard.
Very large integers make trial division slower in the browser. The cap keeps the page responsive while still covering typical coursework and practise values.
Use it to check factor trees or divisor lists you did by hand. Teachers usually want your steps; this confirms the final product-of-primes form.
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