How to prove that these groups are isomorphic (or not)?

Question

I have these following groups.

1. ($\mathbb{Z}/14\mathbb{Z},+) \times(\mathbb{Z}/15\mathbb{Z},+)$ and $(\mathbb{Z}/10\mathbb{Z},+) \times (\mathbb{Z}/21\mathbb{Z},+)$

2. ($\mathbb{Z}/13\mathbb{Z}\backslash$ {0}$,\cdot)$ and ($\mathbb{Z}/21\mathbb{Z}\backslash$ {0}$,\cdot)$

For the first question, I tried to reduce them using gcd(14,7)=2 and gcd(21,15) = 3, which give me ($\mathbb{Z}/7\mathbb{Z},+) \times (\mathbb{Z}/2\mathbb{Z},+) \times(\mathbb{Z}/5\mathbb{Z},+) \times (\mathbb{Z}/3\mathbb{Z},+) $ and $(\mathbb{Z}/5\mathbb{Z},+) \times (\mathbb{Z}/2\mathbb{Z},+)\times (\mathbb{Z}/7\mathbb{Z},+) \times (\mathbb{Z}/3\mathbb{Z},+)$ With the chinese remainder theorem, we can conclude that they are isomorphic.

For the second,

$(\mathbb{Z}/21\mathbb{Z}\backslash$ {0}$,\cdot) \cong (\mathbb{Z}/3\mathbb{Z}\backslash$ {0}$,\cdot) \times (\mathbb{Z}/7\mathbb{Z}\backslash$ {0}$,\cdot)$ with the chinese remainder theorem but I don't know what to do after that.

Can someone give me some hints please?

Thanks!