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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 $\phi(1200)$?

 Jul 18, 2024
 #1
avatar+1926 
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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! :)

 Jul 18, 2024
edited by NotThatSmart  Jul 18, 2024

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