What is the order of the element $14+\langle8\rangle$ in the factor group $\mathbb Z_{24}/\langle8\rangle$.

Question

What is the order of the element $14+\langle8\rangle$ in the factor group $\mathbb Z_{24}/\langle8\rangle$.

Answer 1

Note that the order of an element of a factor group divides the order of the whole group . That is the order of $14+<8>$ divides the order of $\mathbb{Z}_{24}$. You might need this to solve the question. :)

http://www.proofwiki.org/wiki/Order_of_Element_in_Quotient_Group