The H.C.F. (by prime factorization method) of 84, 144 is __________.

Now, of two or more numbers will be the product of common prime factors with the lowest exponential power.

Prime factorisation of 84 and 144 can be seen below:

84 = 2 × 2 × 3 × 7 and, 

144 = 2 × 2 × 2 × 2 × 3 × 3. 

As we can see, 84 and 144 have common prime factors.

Hence, the HCF of 84 and 144 is 2 × 2 × 3 = 12.