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UKMT Senior Mathematical Challenge, 2019 Difficulty 2.0 Junior Find the answer United Kingdom
One of the following is the largest square that is a factor of 10 ! 10! 10 ! n ! = 1 × 2 × 3 × ⋯ × ( n − 1 ) × n n! = 1 \times 2 \times 3 \times \cdots \times (n-1) \times n n ! = 1 × 2 × 3 × ⋯ × ( n − 1 ) × n
(A) ( 4 ! ) 2 (4!)^2 ( 4 ! ) 2 ( 5 ! ) 2 (5!)^2 ( 5 ! ) 2 ( 6 ! ) 2 (6!)^2 ( 6 ! ) 2 ( 7 ! ) 2 (7!)^2 ( 7 ! ) 2 ( 8 ! ) 2 (8!)^2 ( 8 ! ) 2
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