+789 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 ϕ(2835)?
+1950 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∗23∗45∗67=2835⋅2⋅4⋅61⋅3⋅5⋅7=1296
So 1296 is our answer.
I'm not sure if I did this correctly...
Thanks! :)
+1950 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∗23∗45∗67=2835⋅2⋅4⋅61⋅3⋅5⋅7=1296
So 1296 is our answer.
I'm not sure if I did this correctly...
Thanks! :)
+1950 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
