ggT-Rechner
The detailed guide below is currently available in English.
The Euclidean algorithm, briefly
The greatest common factor is the largest whole number that divides every input with nothing left over. Rather than testing every candidate, the Euclidean algorithm replaces the pair again and again: divide a by b, keep the remainder, and repeat with (b, remainder). For 48 and 18 that runs 48 mod 18 = 12, then 18 mod 12 = 6, then 12 mod 6 = 0 — so the GCF is 6. It finishes in very few steps even for huge numbers, which is why this calculator answers instantly. When the GCF comes out as 1, the numbers share no factor beyond 1 and are called coprime.
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What is the GCF used for?
Mostly simplifying fractions and ratios: dividing both parts by the GCF reduces 16/24 to 2/3 in one step. It also sizes grid layouts — tiles of GCF inches fit both room dimensions evenly.
Does it work with more than two numbers?
Yes. Enter an optional third number and the calculator takes the GCF of the first pair, then of that result and the third number — the order never matters.