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
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.