smc

Let the progression start at $a$, have common difference $2$, and end at $a+2(n-1)$. The average term is $\frac{a+(a+2(n-1))}{2}$, or $a+n-1$. Since the number of terms is $n$, and the sum of the terms is $153$, we have: $n(a+n-1)=153$ Since $n$ is a positive integer, it must be a factor of $153$. This means $n=1,3,9,17,51,153$ are the only possibilities. We are given $n>1$, leaving the other five factors. We now must check if $a$ is an integer. We have $a=\frac{153}{n}+1-n$. If $n$ is a factor of $153$, then $\frac{153}{n}$ will be an integer. Adding $1-n$ wil keep it an integer. Thus, there are $5$ possible values for $n$, which is answer $\boxed{5}$.