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Q. Number of ways in which $38808$ can be expressed as a product of two co-prime factors is

Permutations and Combinations

Solution:

$38808=2^{3} \times 3^{2} \times 7^{2} \times 11^{1}$
number of co-prime factors $=2^{\alpha-1}$
where $\alpha$ is number of different Prime factor, here $\alpha=4$
So, number of co-prime factors $=2^{4-1}=8$