AMC / AIME · Prime Factorization · Hard

Prime Factorization: Find the least math such that math is divisible by math.

Unique factorization.

Try the problem

Find the least nn such that n!n! is divisible by 28332^8 3^3.

Hint and answer

Concept to use

Trailing zeros style mid.

Hint

Work with the exponents in the prime factorizations.

Answer

10

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