In 1897, German mathematician August Leopold Crelle published a book listing all the products of pairs of 3-digit numbers. He offered it as a useful aid in the multiplication of large numbers. Suppose we want to multiply 26457081 by 247183. Divide each factor into 3-digit “chunks”: 026 457 081 and 247 183. Now think of each full chunk as a digit — instead of falling in the range 0-9, here each falls in the range 000-999; in effect we’re expressing each factor in base 10³. With that understanding we can proceed with the arithmetic in the usual fashion. The first few partial products are 183 × 081 = 14823, 183 × 457 = 83631, and 183 × 026 = 4758; indent these successively by three places, as shown below, and continue with the rest, following the same pattern:

       26457081
       x 247183

       20007
   112879 14823
  6422 83631
     4758

  6539740652823

The user can look up all the intermediate products in Crelle’s book, so all that remains is to do the final sums. Crelle gives some further examples in the book.

In 1989, Northwestern University mathematician R.P. Boas pointed out that the same method can be used to work through ungainly problems such as 2849365028828173 × 4183920538293052 = 11921516865208167208145227753996 even on a simple 8-digit calculator, the prevailing tool at the time. Cutting these factors into 4-digit chunks reduces all the intermediate products and sums to manageable size, and the 32-digit result is reached reliably even though it would normally be beyond the calculator’s capacity.

(R.P. Boas, “Multiplying Long Numbers,” Mathematics Magazine 62:3 [June 1989], 173-174.)