I was studying Karatsuba multiplication where the complexity is reduced as compared to classical algorithm by splitting each number into two parts.

Now I'm trying to understand how the multiplication will take place when a number is divided into three parts instead of two.

I tried to solve the math but only came up with more number of multiplications than in Karatsuba.

Can someone help me out with this problem?

  • $\begingroup$ Donald Knuth, The Art of Computer Programming. $\endgroup$
    – gnasher729
    Commented Oct 16, 2017 at 6:31
  • 1
    $\begingroup$ Have you checked the Wikipedia page on Karatsuba's algorithm? $\endgroup$ Commented Oct 16, 2017 at 7:47

1 Answer 1


The algorithm you are looking for seems to be the Toom-3 algorithm.

  • $\begingroup$ (And to begin thinking about factors of dissimilar magnitude, check out "Toom-Cook-2.5"/"Toom32".) $\endgroup$
    – greybeard
    Commented Oct 16, 2017 at 8:47

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