Find the H.C.F of 24 and 32.

Given numbers are $24 \mathrm{and} 32$.

Factors of $24$ are $1, 2, 3, 4, 8, 12 \mathrm{and} 24$.

Factors of $32$ are $1, 2, 4, 8, 16 \mathrm{and} 32.$

Common factors of $24 \mathrm{and} 32$ are $1, 2, 4 \mathrm{and} 8$.

The highest common factor of $24 \mathrm{and} 32$ is $8$.

Hence, the correct answer is option C.