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How many perfect square factors does the number 46,656 have?

 Apr 24, 2020
 #1
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0

The number 46656 has 24 square factors.

 Apr 26, 2020
 #2
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+1

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.

 Apr 26, 2020
 #3
avatar
+1

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.


 

 Apr 26, 2020

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