The number of positive divisors of $2^{3} 3^{5} 5^{7} 7^{9}$ which are not perfect squares

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Solution

perfect squares of
$2^{3} : 0, 2 = 2$
$3^{5} : 0, 2, 4 = 3$
$5^{7} : 0, 2, 4, 6 = 4$
$7^{9} : 0, 2, 4, 6, 8 = 5$
total number of positive divisors which are perfect square =120
total divisors =1920
divisors which are not perfect square=1800

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