Maths Olympiad Prep

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, 2019

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

One of the following is the largest square that is a factor of 10!10!. Which one? Note that, n!=1×2×3×⋯×(n−1)×nn! = 1 \times 2 \times 3 \times \cdots \times (n-1) \times n.

(A) (4!)2(4!)^2 (B) (5!)2(5!)^2 (C) (6!)2(6!)^2 (D) (7!)2(7!)^2 (E) (8!)2(8!)^2

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