How many perfect square factors does the number 46,656 have?
The number 46656 has 24 square factors.
46656=2^6 * 3^6
1
2*2
2*2*3*3
2*2*3*3*3*3
2*2*3*3*3*3*3*3
2*2*2*2
2*2*2*2*3*3
2*2*2*2*3*3*3*3
2*2*2*2*3*3*3*3*3*3
2*2*2*2*2*2*2
2*2*2*2*2*2*2*3*3
2*2*2*2*2*2*2*3*3*3*3
2*2*2*2*2*2*2*3*3*3*3*3*3
3*3
3*3*3*3
3*3*3*3*3*3
I only count 16. Maybe I missed some.
a=46656; 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, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216)>>Total P^2 = 16 factors.
+35 
