How to make AppleScript count exactly?
The command line utility bc is capable of arbitrary precision mathematics, and you can call a command line utility from AppleScript and get a value from it.

For example:

set myVariable to do shell script "echo \"89723443578920345892 / 2\" | bc"


Gives this result: 44861721789460172946

To pass command line arguments as AppleScript variables:

set myNumber1 to "89723443578920345892"
set myNumber2 to "2"
set myVariable to do shell script "echo " &amp; myNumber1 &amp; " / " &amp; myNumber2 &amp; "| bc"


But this gets us back to the original problem, AppleScript represents large numbers as a float, so I had to pass the value as a string. So depending on where you get the very large number from, this could be problematic or a non-solution.