Uses the multiplicative recurrence \(\binom{n}{k} = \prod_{i=1}^{k} (n-k+i)/i\), in which every partial product is exactly divisible by \(i\). That keeps the whole computation inside multiplication and small division, and never needs long division.
Details
choose() in base R returns 100891344545563076171808112640 for
\(\binom{100}{50}\); the exact value is
100891344545564193334812497256, so the two differ from the
thirteenth significant digit.