jmc

We begin by realizing that the largest power of $7$ which is less than $441$ is $7^3=343$, and the greatest multiple of $343$ which is less than $441$ is $1\cdot 343=343$. We then have $441=1\cdot 343+98$. Now, we consider the remainder $98$. The largest power of $7$ that is less than $98$ is $7^2=49$ and $98=2\cdot 49$. There is no remainder so we have $$441=1\cdot 7^3+2\cdot 7^2+0\cdot 7^1+0\cdot 7^0.$$Therefore, our base $7$ representation of $441_{10}$ is $\boxed{1200_7}$.