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.
Prime factorisation (UK spelling) or prime factorization (US) is a core skill from middle school through GCSE and early algebra: rewrite an integer as a product of primes raised to powers. This article outlines the idea without heavy jargon and points to our calculator page for fast, transparent checks once you understand the rule.
A prime number has exactly two positive divisors—1 and itself. The Fundamental Theorem of Arithmetic says every integer n > 1 can be written uniquely as a product of primes if you ignore order. Powers save space: repeated division by the same prime becomes an exponent, so structured answers match textbook mark schemes in both metric-first UK courses and typical US curricula.
For primes p1,…,pk and positive integers a1,…,ak: n = p1^a1 × p2^a2 × … × pk^ak. Uniqueness means there is only one multiset of primes and exponents that works for each n.
Take 360. Divide out 2 until it no longer fits: 360 → 180 → 90 → 45, so three factors of 2. Then 45 ÷ 3 → 15 → 5 gives two factors of 3. Finally 5 is prime. Hence 360 = 2³ × 3² × 5. The exponent line is what many examiners expect after a factor tree.
Open the Prime Factorization calculator, type one whole number ≥ 2 in the Positive integer box, then read the printed lines: the product-of-primes string with caret exponents, how many distinct primes appear, and the total prime factors counted with multiplicity (adds duplicate primes like the three copies of 2 in 360). If you leave decimals, negatives, or values under 2, you will see a plain-English correction instead of a result.
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