Prime & Factorization
Check whether a number is prime, find its complete prime factorisation, list all divisors, and find the nearest prime numbers. Prime divisors are highlighted in the divisor list.
Every integer ≥ 2 can be uniquely expressed as a product of primes (Fundamental Theorem of Arithmetic). This uniqueness is the foundation of modern cryptography — large primes are easy to multiply but extremely hard to factor.
A prime number is divisible only by 1 and itself. 2, 3, 5, 7, 11, 13… are the first few primes. 1 is not prime by definition.
Every composite number can be expressed as a unique product of prime factors (Fundamental Theorem of Arithmetic). For example: 360 = 2³ × 3² × 5.
All integers that divide evenly into the number. The number of divisors can be calculated from the prime factorisation: multiply (each exponent + 1). For 360 = 2³×3²×5¹, divisors = (3+1)(2+1)(1+1) = 24.
- •All even numbers greater than 2 are composite. All primes except 2 are odd.
- •If a number's digits sum to a multiple of 3, it's divisible by 3.
- •Prime factorisation is the foundation of RSA encryption — large primes are extremely hard to factor.