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 $\phi(2835)$?

LiIIiam0216 Jul 24, 2024

#1**+1 **

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, and 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! :)

NotThatSmart Jul 25, 2024