18. The operation $\diamond$ is defined on two positive whole numbers as the number of distinct prime factors of the product of the two numbers. For example $8 \diamond 15=3$.
What is the cube of the value of $(720 \diamond 1001)$ ?
SolUtion
216

We have the prime factorisations $720=2^{4} \times 3^{2} \times 5$ and $1001=7 \times 11 \times 13$. Therefore $720 \times 1001$ will have 6 distinct prime factors (namely $2,3,5,7,11$ and 13). The cube of $(720 \diamond 1001)$ is $6^{3}=216$.