Why the factorisation is unique
The fundamental theorem of arithmetic says every whole number above 1 is a product of primes in exactly one way, ignoring order. 360 is 2³ × 3² × 5 and nothing else — there is no second combination that works. That uniqueness is what makes prime factorisation useful rather than merely possible: it is a fingerprint.
Counting divisors without listing them
Once you have the exponents, the number of divisors follows immediately: add one to each exponent and multiply. For 360 = 2³ × 3² × 5¹ that is 4 × 3 × 2 = 24 divisors, and you never had to write any of them down.
This is also why highly composite numbers like 12, 60 and 360 show up in clocks, angles and old currencies — small size, unusually many divisors, so they divide evenly in lots of ways.
The limit on this page
Factoring is done by trial division, which is fast for everyday numbers and slow for large semiprimes. The cap of ten billion keeps the page responsive; beyond it a browser would freeze while working. That difficulty is not a flaw — it is the property RSA encryption is built on.
Frequently asked questions
Is 1 a prime number?
No. Primes have exactly two distinct divisors, and 1 has only one. Excluding it is also what keeps factorisations unique — if 1 counted, you could insert it endlessly.
Is anything uploaded?
No. The factorisation runs in your browser and is not logged.
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