Are Elements of Z/60 Invertible Based on GCD with 60?

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SUMMARY

The elements of Z/60 that are invertible are those whose greatest common divisor (GCD) with 60 is 1. This means that any integer a in the set Z/60 is invertible if gcd(a, 60) = 1. The specific elements that meet this criterion can be identified through the use of the Euclidean algorithm or by listing integers from 1 to 59 and checking their GCD with 60. The inverses of these elements can be computed using the Extended Euclidean Algorithm.

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sukichk
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which elements of Z/60 are invertible?? what are their inverses?

do we have any quick way to do this kind of question??
 
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Hint: gcd(n, 60).
 

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