Total number of divisors of $N = 3^{5} {.5}^{7} {.7}^{9}$ that are of the form $4 n + 1, n \geq 0$ is

15

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30

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120

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240

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Solution

The correct option is D $240$
$\begin{matrix} N = 3^{5} 5^{7} 7^{9} 4 n + 1, n > 0 n = 01 n = 15 h = 29 h = 313 = \frac{(5 + 1) (7 + 1) (9 + 1)}{2} = \frac{6 \times 8 \times 10}{2} = 240 \end{matrix}$

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