Find the prime factorisation of any number with step-by-step working. Plus GCD and LCM tools.
A prime factorisation calculator decomposes any positive integer into its unique product of prime numbers. Every integer above 1 has exactly one prime factorisation — the Fundamental Theorem of Arithmetic. This decomposition is the foundation of number theory and underlies modern cryptography (RSA encryption depends on the difficulty of factoring large composites).
Beyond cryptography, prime factorisation is used to find the greatest common divisor (GCD) and least common multiple (LCM) of two numbers, simplify fractions, solve modular arithmetic problems, and check whether two numbers share common factors.
Inputs: Factorise 360
No — primes are defined as integers greater than 1 with exactly two positive divisors (1 and themselves). 1 has only one divisor (itself), so it does not qualify. The exclusion is deliberate: it makes the Fundamental Theorem of Arithmetic clean (unique factorisation up to ordering).
RSA picks two large primes p, q (each ~600+ digits) and publishes their product n = p × q. The encryption is easy to compute knowing only n, but reversing it (extracting the original message) requires factoring n into p and q — a computationally infeasible task for sufficiently large primes. The security of nearly all current internet banking and HTTPS rests on this asymmetry.
EMI Calculator Mortgage Calculator SIP Calculator Compound Interest GST / VAT Calculator Salary Calculator Unit Converter Currency Converter Scientific Calculator Concrete Calculator Paint Calculator Tile Calculator Calorie / TDEE Body Fat Macro Calculator O-Ring Sizes Bolt & Nut Sizes Pipe Sizes Wire Gauge AWG Needle Gauge Chart IV Cannula Sizes Suture Sizes Catheter French Sizes Drug Dosage See all 90+ calculators ›