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How many perfect squares are factors of 2 × 4 × 6 × 8 × 10 × 12?

 May 22, 2020
 #1
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Factoring these numbers:  2  =  21

                                           4  =  22

                                           6  =  2 x 3

                                           8  =  23

                                         10  =  2 x 5

                                         12  =  22 x 3

Combining:  210 x 32 x 5

 

Perfect squares must have even powers; therefore, none will contain the single 5.

 

Possible perfect squares:

        22,   22·32,   24,   24·32,   26,   26·32,   28,   28·32,   210,   210·32

 May 22, 2020
 #2
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a=46080; c=(1); n=2; s=2#a;cycle:d=a/n^2;if(a%n^2==0, c=sort(c,n),0);n++;if(n<=s, goto cycle, c);printc,;print">>Total P^2 =", count c;print;print;

 

 

OUTPUT: (1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96)>>Total P^2 = 12  Note: You must square these numbers to get 12 perfect squares that are factors of 46,080.


 

 May 22, 2020
edited by Guest  May 22, 2020

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