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What is the smallest positive (n) for which (n!) is divisible by (1440)?सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या (1440) से विभाज्य हो?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (8)(8)
(1440=2^5\cdot3^2\cdot5), and this requirement is first satisfied by (8!). For divisibility, check prime factors.(1440=2^5\cdot3^2\cdot5) है और यह जरूरत पहली बार (8!) में पूरी होती है। विभाज्यता में अभाज्य गुणनखंड जांचें।
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