CAT 2022 Number System Question (Hard)

Question

For some natural number , assume that ! is divisible by . The largest possible value of is

Accepted Answer

Strategy We are to find the largest such that n! leq 15000 Because after that point, will no longer be within , since contains factors up to , and that should not exceed . --- Step-by-Step We want to find the largest such that n! leq 15000 Compute factorials step by step Notice Thus, is the largest

CAT 2022

Quantitative

Number System

Hard

For some natural number $n$ , assume that $(15,000)$ ! is divisible by $(n !) !$ . The largest possible value of $n$ is

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