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How many positive perfect cube factors does 3^6*5^{10} have?

 Jun 22, 2018
 #1
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3^6*5^{10}

=7119140625 = 3^6 * 5^10

From factoring above, you will have: 3^3, 3^6, 5^3, 5^6, 5^9 =27,  729, 125, 15625, 1953125=5 perfect cubes.

 Jun 22, 2018
 #2
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I don't think thats right because 5^3*3^3 is also a cube.

 Jun 22, 2018
 #3
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You are right! Was too hasty!. 3^3 x 5^3, 3^3 x 5^6, 3^3 x 5^9, 3^6 x 5^3, 3^6 x 5^6, 3^6 x 5^9=

3375, 421875, 52734375, 91125, 11390625, 1423828125

 

I think I got them all: 5 + 6 = 11 perfect cubes? Since you know what to do, you can check them and see if I missed any.

 Jun 22, 2018

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