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 $\phi(1200)$?

AnswerscorrectIy Jul 15, 2024

#1**+1 **

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! :)

NotThatSmart Jul 18, 2024