Write 360 as 2³ × 3² × 5 and you have its prime factorization in exponent form — the compact fingerprint no other number shares. Getting there is a patient division drill: divide by the smallest prime that fits, write it down, and repeat on the quotient until you reach 1. For 360: ÷2 → 180, ÷2 → 90, ÷2 → 45, ÷3 → 15, ÷3 → 5, ÷5 → 1, giving 2 × 2 × 2 × 3 × 3 × 5, or 2³ × 3² × 5. The exponent form is more than tidiness — it makes the divisor count obvious (multiply each exponent-plus-one: 4 × 3 × 2 = 24 divisors) and the GCD/LCM recipes mechanical.

Cryptographers care because factoring a 600-digit semiprime would outlast the universe, which is exactly what protects RSA keys. Teachers care because it is the gateway to fraction work: 48 = 2⁴ × 3 and 180 = 2² × 3² × 5 share 2² × 3, so their GCD is 12. Use this calculator to verify a completed factorization: multiply the prime powers on paper into two groups — for 360, 2³ = 8 and 3² × 5 = 45 — type the first group in the Variable A box (8) and the second in the Variable B box (45). The Result box shows 360, confirming the exponents and primes are all correct.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Prime Factorization Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.