Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Prime Factorization
Factorial
Divisibility

Formulas

n divides m! if and only if m! contains all prime factors of n with the required multiplicities
Maximum Power of p in n! = ∑ ⌊n/p^k⌋ for k ≥ 1 until ⌊n/p^k⌋ = 0

Theorems

Prime Factorization Theorem
Divisibility Rules

Suitable Grade Level

Grades 10-12