Calculate the invariant factors of the group $G=\mathbb Z_{12} \oplus \mathbb Z_{21} \oplus \mathbb Z \oplus \mathbb Z \oplus \mathbb Z_{20} \oplus \mathbb Z_{9} \oplus \mathbb Z_7$.
Applying the chinise remainder theorem and rearranging coefficients, I've arrived to $$G=\mathbb Z^2 \oplus \mathbb Z_3 \oplus \mathbb Z_{84} \oplus \mathbb Z_{1260}$$ Notice that $3| \space84| \space1260$. Would the invariant factors be $\langle 3 \rangle, \langle 84 \rangle$ and $\langle 1260 \rangle$? It may seem a very basic doubt but since I am just learning this stuff I would like to know I am getting things right. Thanks in advance.