Solving for Integers a and b in a Divisibility Equation

[clueles]

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

 

[Data]

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?)?

 

[clueles]

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

 

[shmoe]

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.