Solving for Integers a and b in a Divisibility Equation

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a = 238000 = 2^4 x 5^3 x 7 x 17 and b = 299880 = 2^3 x 3^2 x 5 x 7^2 x 17

is there an integer n so that a divides b^n if so what is the smallest possibility for n
 
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What criterion are needed for one positive integer to divide another, if both of them are greater than 1 (Hint: Might prime factorizations have something to do with it?)?
 
i'm sorry i really don't follow your explanation. my guess that you have to divide the factorizations and that could possibly give you the answer
 
Was another thread on the same topic necessary?

Here's a simpler question, for what values of k does 2^4 divide 2^k?

For what values of k and l does (2^4)x(5^3) divide (2^k)x(5^l)?

If you can answer these, you should be able to handle your question.
 

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