The function f(n) is defined for all positive integers n, where n > 1, as the product of n consecutive positive multiples of n. How many zeros does f(100) end with?

Correct answer marked below

143

224

Correct

2400

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Official Explanation

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Let's break down the question:

According to the problem, f(100) is the product of 100 consecutive positive multiples of 100.

So: f(100) =

100 \times 200 \times 300 \times \ldots \times 10,000

(100 \times 1) \times (100 \times 2) \times (100 \times 3) \times \ldots \times (100 \times 100)

100^{100} \times 100!

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.