Factorial of Smallest Multiple!

Find the smallest positive integer value of x x such that ( 349 x ) ! (349x)! is divisible by 34 9 350 349^{350} .

If there is no such positive integer value x x , then enter 0.

Is constructing a generalization possible after replacing 349 349 by any prime p p and 350 350 by p + 1 p+1 ? If No , why?


The answer is 349.

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1 solution

Kushal Bose
Nov 29, 2016

Here 349 349 will be the answer because in each multiple of 349 there is only one factor of 349 available.In the last rem 349 × 349 349 \times 349 we get one more extra 349 349 .So,total become 349 + 1 = 350 349+1=350 .

Yes it is possible to generalize for any prime p p because no number will prime number untill it is the factor of that prime

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