In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length n\documentclass[12pt]{minimal}
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\begin{document}$$n$$\end{document} over a finite field Fq\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_q$$\end{document}, in the case which each prime divisor of n\documentclass[12pt]{minimal}
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\begin{document}$$n$$\end{document} is also a divisor of q-1\documentclass[12pt]{minimal}
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\begin{document}$$q-1$$\end{document}.