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How many even perfect square factors does 2^4*7^9 have?

MIRB16  Apr 28, 2018

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 #1
avatar+92441 
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How many even perfect square factors does 2^4*7^9 have?

 

From the considerations below I  can see the answer is 10

         
\(7^2, \qquad 7^4, \qquad 7^6,\qquad 7^8 \qquad \text{none of these are even } \\~\\ \\ \text{all those below are even}\\ 2^2, \qquad 2^2*7^2, \qquad 2^2*7^4, \qquad 2^2*7^6,\qquad 2^2*7^8 \\ 2^4, \qquad 2^4*7^2, \qquad 2^4*7^4, \qquad 2^4*7^6,\qquad 2^4*7^8 \\ \)

Melody  Apr 28, 2018
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 #1
avatar+92441 
+4
Best Answer

How many even perfect square factors does 2^4*7^9 have?

 

From the considerations below I  can see the answer is 10

         
\(7^2, \qquad 7^4, \qquad 7^6,\qquad 7^8 \qquad \text{none of these are even } \\~\\ \\ \text{all those below are even}\\ 2^2, \qquad 2^2*7^2, \qquad 2^2*7^4, \qquad 2^2*7^6,\qquad 2^2*7^8 \\ 2^4, \qquad 2^4*7^2, \qquad 2^4*7^4, \qquad 2^4*7^6,\qquad 2^4*7^8 \\ \)

Melody  Apr 28, 2018

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