Editing Multiplication algorithm (section)

===Example===
This example uses ''long multiplication'' to multiply 23,958,233 (multiplicand) by 5,830 (multiplier) and arrives at 139,676,498,390 for the result (product).
       23958233
 ×         5830
 ———————————————
       00000000 ( =  23,958,233 ×     0)
      71874699  ( =  23,958,233 ×    30)
    191665864   ( =  23,958,233 ×   800)
 + 119791165    ( =  23,958,233 × 5,000)
 ———————————————
   139676498390 ( = 139,676,498,390)

====Other notations====
In some countries such as [[Germany]], the above multiplication is depicted similarly but with the original product kept horizontal and computation starting with the first digit of the multiplier:<ref>{{Cite web |title=Multiplication |url=http://www.mathematische-basteleien.de/multiplication.htm |access-date=2022-03-15 |website=www.mathematische-basteleien.de}}</ref> 

 23958233 · 5830
 ———————————————
    119791165
     191665864
       71874699
        00000000
 ———————————————
    139676498390

Below pseudocode describes the process of above multiplication. It keeps only one row to maintain the sum which finally becomes the result. Note that the '+=' operator is used to denote sum to existing value and store operation (akin to languages such as Java and C) for compactness.

<syntaxhighlight lang="pascal" line>
multiply(a[1..p], b[1..q], base)                            // Operands containing rightmost digits at index 1
  product = [1..p+q]                                        // Allocate space for result
  for b_i = 1 to q                                          // for all digits in b
    carry = 0
    for a_i = 1 to p                                        // for all digits in a
      product[a_i + b_i - 1] += carry + a[a_i] * b[b_i]
      carry = product[a_i + b_i - 1] / base
      product[a_i + b_i - 1] = product[a_i + b_i - 1] mod base
    product[b_i + p] = carry                               // last digit comes from final carry
  return product
</syntaxhighlight>