About the prime factorization calculator
This free prime factorization calculator finds the prime factors of any positive integer greater than or equal to 2. You enter a number, click Get result, and the tool shows its prime factorization—the unique product of prime numbers that multiply to give your number. For example, 24 = 2 × 2 × 2 × 3 and 360 = 2 × 2 × 2 × 3 × 3 × 5. The calculator also lists the distinct prime factors (each prime that appears, without repetition). No sign-up or download is required; it runs in your browser and is designed to be mobile-friendly and responsive.
Prime factorization is fundamental in number theory and useful in many areas of math and applied subjects. A prime number is a whole number greater than 1 whose only positive divisors are 1 and itself (e.g. 2, 3, 5, 7, 11). The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be written uniquely as a product of primes (up to the order of the factors). This calculator uses trial division: it repeatedly divides the number by the smallest possible prime (starting with 2) and collects the factors until the quotient is 1. The result is the prime factorization in expanded form.
Prime factorization is used to find the greatest common divisor (GCD) and least common multiple (LCM) of two or more numbers, to simplify fractions by canceling common factors, to work with roots and exponents in algebra, and in cryptography (e.g. the security of RSA relies on the difficulty of factoring large numbers). In school math, it appears when reducing fractions to lowest terms, finding LCM and GCD, and understanding divisibility. Teachers and students use prime factorization to build number sense and prepare for algebra and number theory.
To use this calculator, type a positive integer (e.g. 24, 100, 12345) and click Get result. Only whole numbers 2 and above are valid; decimals and negative numbers are not used in prime factorization. For very large numbers, the calculation may take a moment because the algorithm checks possible prime divisors up to the square root of the number. The output shows the full product (e.g. 24 = 2 × 2 × 2 × 3) and the list of distinct primes (2, 3). You can use it for homework, teaching, or quick checks when working with factors, multiples, GCF, or LCM.
This prime factorization calculator is free, works on phones and tablets, and shows the result in a clear, readable format. For related tools, try our GCF or LCM calculators once you have the prime factorizations of two or more numbers. Understanding prime factorization is a key step toward mastering divisibility, fractions, and number theory.