सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या \(2^8\cdot3^2\cdot5^2\) से विभाज्य हो?
What is the smallest positive (n) for which (n!) is divisible by \(2^8\cdot3^2\cdot5^2\)?
Explanation opens after your attempt
Correct Answer
C. (10)
Concept
(10!) contains exponent (8) of (2) and exponent (2) of (5). (9!) does not contain \(5^2\), so (10) is minimum.
Why this answer is correct
The correct answer is C. (10). (10!) contains exponent (8) of (2) and exponent (2) of (5). (9!) does not contain \(5^2\), so (10) is minimum.
Exam Tip
(10!) में (2) की घात (8) और (5) की घात (2) मिलती है। (9!) में \(5^2\) नहीं आता, इसलिए (10) न्यूनतम है।
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