For how many different digits $n$ is the two-digit number $\underline{6}\underline{n}$ divisible by $n$? (The expression $\underline{6}\underline{n}$ should be interpreted as a two-digit integer with tens digit 6 and units digit $n$, not as 6 times $n$.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For how many different digits $n$ is the two-digit number $\underline{6}\underline{n}$ divisible by $n$? (The expression $\underline{6}\underline{n}$ should be interpreted as a two-digit integer with tens digit 6 and units digit $n$, not as 6 times $n$.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
For how many different digits $n$ is the two-digit number $\underline{6}\underline{n}$ divisible by $n$? (The expression $\underline{6}\underline{n}$ should be interpreted as a two-digit integer with tens digit 6 and units digit $n$, not as 6 times $n$.)
train