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How many factors of ********** are even numbers?

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How many factors of ********** are even numbers?
posted Feb 1, 2018 by anonymous

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1 Answer

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********** = 73^2 *37^2* 17^1 * 5^1 * 3^4 * 2^4

Any factor of this number should be of the form 73^a * 37^b * 17^c * 5^d * 3^e * 2^f

For the factors of this number to be an even number f should be non 0

a can take values 0, 1, 2,
b can take values 0, 1, 2
c can take values 0, 1
d can take values 0, 1
e can take value 0, 1, 2, 3, 4
f can take value 1, 2, 3, 4

Total number of even factors = 3*3*2*2*5*4= 720

answer Feb 2, 2018 by Yasin Hossain Siinan
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