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Question 1
$15$ has factors $3$ and $5$ (and $1$ and $15$). Write out all the numbers between $1$ and $14$ inclusive and then cross out everything which is a multiple of $3$, or $5$. You should be left with $8$ numbers which are co-prime with $15$.
Question 2
For example, $\phi(7)=6$ as $1, 2, 3, 4, 5$ and $6$ share no common factors with $7$. If one of the first $6$ numbers did share a factor with $7$, then $7$ would not be prime.
Question 3
For example $\phi(3^2)= 6$ since $1, 2,$ _ $, 4, 5,$ _ $, 7, 8$ are coprime with $9$.
Try a few more examples for different prime numbers and different powers before trying to generalise.
Question 4
$24$ can be written as $3 \times 8$. Is it true that $\phi(24) = \phi(3) \times \phi(8)$?
Alternatively $24$ can be written as $4 \times 6$. Is it true that $\phi(24) = \phi(4) \times \phi(6)$?
Question 5
It might be helpful to write $n$ as a product of prime factors, e.g. $n=p_1^{a_1} \times p_2^{a_2} \times \cdots \times p_k^{a_k}$.