Compute the Euler function $\phi(n)$ for $n = 360$ as well as the number of divisors $d(n)$.

Question

Compute the Euler function $\phi(n)$ for $n = 360 $ as well as the number of divisors $d(n)$.

Is this correct?

$360 = 2^3\cdot 3^2\cdot 5$ thus $\phi(n) = 2^2\cdot 2\cdot 3\cdot 4 = 96$.

$d(n) = 4 \times 3 \times 2 = 24$.

Answer 1

$360 = 2^3\times 3^2\times5$. Since Euler Phi function is multiplicative, $\phi(360)=\phi(8)\times\phi(9)\times\phi(5)=(8-4)\times(9-3)\times4=96.$

Which means you are correct.

Answer 2

You are correct, although note that you're better using \times or \cdot rather than just a space, because in LaTeX (and MathJax) a space will be omitted.

Answer 3

Euler Phi Function is a method for calculation the number of integers less than and co prime to a particular integer.

Let,$n$ be an integer such that $n=p_1^{a_1}\times p_2^{a_2}\times p_3^{a_3}\times...p_n^{a_n}$.

$\phi(n)=n(1-\frac{1}{p_1})(1-\frac{1}{p_2})...(1-\frac{1}{p_n})$

Just plug in the values to get your answer.