Extreme Expansion Factorials
GMAT glossary · Playbook
Definition
Cancel a large factorial ratio by expanding only the larger factorial down to the smaller one, then finish with primes if needed.
Extreme Expansion Factorials in plain English
Pull Extreme Expansion Factorials when comparing or canceling huge factorials like (2n)!/(n!). Clues include (2n)!, ratio of factorials, cancel factorial. Blueprint: Expand only the larger factorial down to the smaller one, cancel matching factors, then finish with primes or Legendre if needed. Why it beats the long way: Writing every factor of both sides is wasteful; cancel first, count primes second. Micro-example: ((2n)!)/(n!) at n=4: expand (8)! down to 4! as 8· 7· 6· 5· 4!, cancel 4!, and finish 8· 7· 6· 5 = 1680 without writing both full factorials.
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