+1216 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 $\phi(1200)$?
+1950 Let's set up for a really cool function.
First, note that
1200=12∗52∗22=24∗3∗52
Now, we use Euler's Totient Function. We have
ϕ1200=1200/(2∗3∗5)∗(2−1)(3−1)(5−1)=40(1)(2)(4)=320
The answer is 320
Thanks! :)
