Find the biggest number which can divide both 324 and 144.

Given:
The numbers 324 and 144.

Formula Used:
Prime factorization of each number and the common factors.

Solution:
Prime factorization of 324:

​$$324 = 2^2 \times 3^4$$

Prime factorization of 144:

$$144 = 2^4 \times 3^2$$​ ​​

The common factors are the minimum powers of the common prime factors:

For 2, the minimum power is $$2^2.$$​
For 3, the minimum power is $$3^2$$​.

GCD =  $$2^2 \times 3^2 = 4 \times 9 = 36$$

Thus, the correct answer is (b).​​