I'm not sure division really is harder; I think it's just that the common algorithm for division is harder. DanielV's answer points out that if you calculate via a table of logarithms, multiplication and division are equally easy. (Or equally difficult, I suppose.) The so-called “russian peasant algorithm” for multiplication has a corresponding algorithm for division that is almost identical, neither easier nor harder. To calculate $23\times 57$ with this algorithm, we write two columns of numbers, starting with $1$ and $23$, and each line contains numbers that are twice the previous line:

$$\begin{array}{crr}
& 1 & 23 \\
& 2 & 46 \\
& 4 & 92 \\
& 8 & 184 \\
& 16 & 368 \\
& 32 & 736 \\
\end{array}$$

Then we mark the rows with stars so that the left-hand numbers add up to $57$. We do this by subtracting the left-hand numbers successively from 57, starting at the bottom, until the total reaches 0:

$$\begin{array}{crr}
* & 1 & 23 & 1\\
& 2 & 46 \\
& 4 & 92 & \\
* & 8 & 184 & 9\\
* & 16 & 368 & 25\\
* & 32 & 736 & 57\\
\end{array}$$

(Here $57-32 = 25; 25-16 = 9; 9-8=1, $ and $1-1=0$.)

Finally we add the numbers from the middle column in the starred rows, obtaining $23\times 57 = 23 + 184 + 368 + 736 = 1311$.

To perform division is almost the same. To divide $1370$ by $29$ we write two columns as before:

$$\begin{array}{crr}
& 1 & 29 \\
& 2 & 58 \\
& 4 & 116 \\
& 8 & 232 \\
& 16 & 464 \\
& 32 & 928 \\
& 64 & 1856 \\
\end{array}$$

Then we subtract the right-hand numbers from $1370$, starting from the bottom, marking the rows where subtraction is possible:

$$\begin{array}{crrr}
*& 1 & 29 & 7\\
* & 2 & 58& 36\\
* & 4 & 116 & 94\\
* & 8 & 232 & 210 \\
& 16 & 464 \\
* & 32 & 928 & 442\\
& 64 & 1856 & 1370\\
\end{array}$$

Then we add the left-hand numbers in the starred rows, obtaining the quotient $1+2+4+8+32 = 47$; the remainder, $7$, is in upper-right-hand corner.