If the number $200!$ is written in the form $p × 10^q$ , where $p$ and $q$ are integers, what is the maximum possible value of $q$ ?

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What this question tests

Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.

Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.

If the number 200!200!200! is written in the form p×10qp × 10^qp×10q, where ppp and qqq are integers, what is the maximum possible value of qqq?