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  4. Consider the number N=10! . If the number of positive divisors of N is λ , then (λ /30) equals

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Q. Consider the number $N=10!$ . If the number of positive divisors of $N$ is $\lambda ,$ then $\frac{\lambda }{30}$ equals

NTA AbhyasNTA Abhyas 2022

Solution:

$10!=2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 7$
Number of divisors $=9\times 5\times 3\times 2=270=\lambda $