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The detailed guide below is currently available in English.
Factors versus prime factors
A factor of a number divides it with no remainder: the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The prime factorization rebuilds the same number purely from primes — 36 = 2² × 3² — and is unique no matter how you break the number down first. The two views connect through arithmetic: multiply each prime’s (exponent + 1) choices together and you get the factor count, here (2 + 1) × (2 + 1) = 9. A number with exactly two factors, 1 and itself, is prime; this calculator flags that for you.
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Is 1 a prime number?
No — by convention 1 is neither prime nor composite, because primes need exactly two distinct factors and 1 has only one. That definition keeps the unique prime factorization rule working.
Why is my even count of factors sometimes odd?
Only perfect squares have an odd number of factors. Square numbers pair their square root with itself — 36 pairs 6 with 6 — which removes one partner from the pairing and leaves an odd total.