We need to check that which of the given options CANNOT be the factor of $\(\left(2^n\right)\left(3^k\right)\)$ where $n$ and $k$ are both positive integers.

The expression $\(\left(2^{\mathrm{n\right)\left(3^{\mathrm{k\right)\)$, where n and k are positive integers, can have only those factors which have only 2 's \& 3's as their prime factors.


(A) $\(8=\left(2^3\right)\)$
(B) $\(24=2^2 \times 3^1\)$
(C) $\(42=2^1 \times 3^1 \times 7^1\)$ as it is has 7 as one of the prime factors, it cannot be a factor of the given expression
(D) $\(72=2^3 \times 3^2\)$
(E) $\(162=2^1 \times 3^4\)$

Hence only (C) CANNOT be a factor of the given expression, so is the correct answer.