Using mnemonic systems, remembering numbers becomes extremely simple.
There are a number of approaches, depending on the types of numbers being remembered:
1. Short numbers
These can be stored in a number of ways:
The easiest, but least reliable, is to use simple Number/Rhyme images associated in a story.
2. Long numbers (e.g. Pi)
This can be remembered using the Journey System. At a simple level, numbers can be stored at each stop on the journey using e.g. the Number/Shape system. The amount of digits stored at each stop can be increased initially by using either the Major System or the Dominic Method, and enhanced still further by using simple techniques to Expand Memory Systems.
Using all the simple techniques in concert, there is no reason why you should not be able to store a 100 digit number with relatively little effort. Using the more powerful systems, holding it to 1000 digits might not be too much of a challenge.