+207 For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(1200)$?
+1908 Let's set up for a really cool function.
First, note that
\(1200 = 12 * 5^2 * 2^2 = 2^4 * 3 * 5^2 \)
Now, we use Euler's Totient Function. We have
\(\phi{1200} = 1200 / ( 2 * 3 * 5) * (2-1)(3-1) (5-1) = 40 (1)(2)(4) = 320 \)
The answer is \(320\)
Thanks! :)
