How many positive integers $\le 462$ are relatively prime to $462$? How many positive integers less than or equal to $462$ are relatively prime to $462$?
My Approach
Well my approach is basically that we find $|A \cup B|$ where:

*

*$A = \{\text{all prime numbers} \le 462\}$

*$B = \{\text{every number which isn't a factor of } 462\}$
I just don't know how to calculate this so it is not an efficient method so please answer with a more efficient method. Thank you!

HINT: Euler's Totient function $\phi$ is multiplicative. In other words, if we have two positive integers $a$ and $b$ with $\gcd(a,b) = 1$, then $\phi(ab) = \phi(a)\phi(b)$. So, you can use prime factorization of $462$ to divide and conquer the problem.
