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What is the least positive integer n such that 1560 divides n^2?

 May 25, 2021
 #1
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The smallest n that works is 44.

 May 26, 2021
 #2
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Factor 1560 into its prime factors:

 

1560 = 2^3*3*5*13

 

To make this into a perfect square multiply by 2*3*5*13 = 390

 

n^2 = 1560*390 = 608400

 

Hence n = 780

 May 26, 2021

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