Solution
Given:
- •The number n is the product of the first 49 natural numbers
•The numbers \(\frac{n}{(24)^p}\) and \(\frac{n}{(36)^q}\) are integers
To find:
•The maximum possible value of p + q
Approach and Working:
- •When it is given that\(\frac{n}{(24)^p}\) is an integer, it necessarily means p is the highest power of 24 that can divide the number n
•In a similar way we can say that, if\(\frac{n}{(36)^q}\) is an integer, then q is the highest power of 36 that can divide the number n
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