Primfaktorzerlegung
The detailed guide below is currently available in English.
Why the prime factorization is unique
Every whole number above 1 factors into primes in exactly one way, no matter how you chop it up first — the fundamental theorem of arithmetic. The trial-division method behind this calculator keeps testing 2, 3, 4, 5… dividing out each prime as many times as it fits: 360 ÷ 2 = 180 ÷ 2 = 90 ÷ 2 = 45, then 45 ÷ 3 = 15 ÷ 3 = 5, leaving 2³ × 3² × 5. Composite divisors never appear because their primes were already removed. The work stops at the square root, since any leftover factor above that point must itself be prime — that is why a trillion factors instantly.
Häufige Fragen
How does the exponent form help me find divisors?
A divisor picks any exponent from 0 up to each prime’s exponent. For 2³ × 3² × 5 that gives 4 × 3 × 2 = 24 possible divisors without listing them, since each exponent has one more choice than its value.
What is the biggest number this can factor?
One trillion (10¹²). Trial division checks factors only up to the square root — a million steps — so it stays fast, but numbers beyond that with huge prime factors would need advanced methods.