Basic Legendre Counting
GMAT glossary · Playbook
Definition
A first-pass Legendre count for the exponent of a prime (often 5 for trailing zeros) inside n!.
Basic Legendre Counting in plain English
Pull Basic Legendre Counting when a first pass at prime exponents in factorials before harder composite asks. Clues include Factors of 2 or 5 in n!, trailing zeros of n!. Blueprint: Apply Legendre once for the needed prime. For trailing zeros use p=5 (usually the limiter). Why it beats the long way: Guessing from small factorials does not scale; one Legendre sum is exact. Micro-example: Trailing zeros of 25!: apply Legendre with p=5 to get lfloor 25/5 rfloor + lfloor 25/25 rfloor = 5 + 1 = 6. Skip expanding 25! entirely.
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