$$P=2^{5} \times 3^{8}$$ and $$Q= 2^{3} \times 3^{K}$$ . If the highest common factor of P and Q is $$2^{3} \times 3^{3}$$ , then what is the value of K?

$$P=2^{5} \times 3^{8}$$    Eq.(i)

$$Q= 2^{3} \times 3^{K}$$    Eq.(ii)

If the highest common factor of P and Q is $$2^{3} \times 3^{3}$$    Eq.(iii)

By comparing Eq.(i), Eq.(ii) and Eq.(iii), the value of K = 3 [Here $$2^{3}$$ is one of the highest common factor of P and Q. Because $$2^{3}$$ is commonly available in the both. Similarly making $$3^{3}$$ is one of the highest common factor of P and Q. It should be commonly available in both.]