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A very large number x is equal to 2^3*4^5*6^7*8^9. What is the smallest positive integer that, when multiplied with x, produces a product that is a perfect square?

 Jul 4, 2022
 #1
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2^3 *  4^5  * 6^7  * 8^9 =

 

2^3 * (2^2)^5  * 2^7 * 3^7 * (2^3)^9  =

 

2^3 * 2 ^10 * 2^7  * 2^27 * 3^7  =

 

2^47 * 3^7

 

We need  2 * 3    =  6

 

 

CORRECTED  !!!!

 

cool cool cool

 Jul 4, 2022
edited by CPhill  Jul 4, 2022
 #2
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1 - The smallest integer ==2 * 3 ==6>>>>>1.846757322198614016e+18 = 2^48 * 3^8

 

2 - The next smallest ==24 = 2^3 * 3

 

3 - The next smallest ==54 = 2 * 3^3

 

4- The next smallest==96 = 2^5 * 3

 Jul 4, 2022

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