+719 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 $\phi(2835)$?
+953 We can use Euler's Totient Function.
Let's find all the distinct prime factors of 2835 first.
The prime factors of 2835 are \(3,5,7\)
Now, we simplfy do \(2835(1-1/3)(1-1/5)(1-1/7)\)
Simplfying this, we have
\(2835 * \frac{2}{3}*\frac{4}{5}*\frac{6}{7} =\frac{2835\cdot \:2\cdot \:4\cdot \:6}{1\cdot \:3\cdot \:5\cdot \:7}=1296\)
So 1296 is our answer.
I'm not sure if I did this correctly...
Thanks! :)
+953 We can use Euler's Totient Function.
Let's find all the distinct prime factors of 2835 first.
The prime factors of 2835 are \(3,5,7\)
Now, we simplfy do \(2835(1-1/3)(1-1/5)(1-1/7)\)
Simplfying this, we have
\(2835 * \frac{2}{3}*\frac{4}{5}*\frac{6}{7} =\frac{2835\cdot \:2\cdot \:4\cdot \:6}{1\cdot \:3\cdot \:5\cdot \:7}=1296\)
So 1296 is our answer.
I'm not sure if I did this correctly...
Thanks! :)
+953 Thanks to you too, CPhill.
I did not know about Euler's Totient Function until today when we did a problem similar earlier.
Sure saved me a lot of time on this one! Lol! :)
Thanks! :)
~NTS
