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# Number Theory

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A very large number x is equal to 2^2*3^3*4^4*5^5*6^6. What is the smallest positive integer that, when multiplied with x, produces a product that is a perfect square?

Apr 22, 2022

#1
+1370
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For the number to be a perfect square, each of its factors must be a power of 2.

To do this, we need a $$3 \times 5 = \color{brown}\boxed{15}$$

Apr 22, 2022

#1
+1370
+2
To do this, we need a $$3 \times 5 = \color{brown}\boxed{15}$$