In $\mathbb{Z_{60}},$ the generators are the numbers $0,\cdots,59$ that are relatively prime to $60.$ These are $1,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59.$
We can write Multipliatively , $G=\langle{a\rangle}$ where the order of $a$ is $60$, the generators are $a^{1},a^{7},a^{11},a^{13},a^{17},a^{19},a^{23},a^{29},a^{31},a^{37},a^{41},a^{43},a^{47},a^{49},a^{53},a^{59}.$
Two positive integers are said to be relatively prime if their greatest common divisor is $1.$ For instance, $10$ and $7$ are relatively prime as they share no factors other than $1.$
$\implies$Note that neither integers need to be prime in order for them to be relatively prime $8$ and 15 are both not prime, yet they are relatively prime.
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