Find the H.C.F of 12, 24 and 36.

Given numbers are $12, 24 \mathrm{and} 36$.

We have to find H.C.F using prime factorization method. So, we have to find prime factors of each number.

Prime factors of $12$ are$: 2 \times 2 \times 3$

Prime factors of $24$ are$: 2 \times 2 \times 2 \times 3$

Prime factors of $36$ are$: 2 \times 2 \times 3 \times 3$

The common factors of $12, 24 \mathrm{and} 36$ are $: 2 , 2 \mathrm{and} 3$.

Therefore, H.C.F of $12, 24 \mathrm{and} 36$ is $2\times 2\times 3=12.$

Hence, the correct answer is option B.