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Find the largest n such that n^2 divides 2000.

 May 23, 2020
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I'm assuming that you mean that the largest int. n,n^2  divides 2000 into a integer, so n^2 is a factor of 2000.

 

Factors of 2000:

 

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000

 

So 2000 isn't a perfect square, nor 1000,

 

500, isn't.

 

400 = 20^2!

 

n = 20.

 

If you don't understand anything feel free to ask.

 May 23, 2020

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