25+ Ways to Multiply

This is a summary of the different ways to multiply, with links to descriptions.  There are also several descriptions on Pat Ballew’s blog.


Formulas and Tables:

Physical Objects:

Other Methods:

33 Responses to “25+ Ways to Multiply”

  1. girl Says:

    you dont have square way???

  2. Ξ Says:

    I’m not sure of what you mean by the square way — the one that comes to mind is the Babylonian formulas. Would you be able to describe the method you’re thinking of? I’d be thrilled to add more to the list!

  3. TwoPi Says:

    “The square way” might also be a reference to grid/lattice multiplication…

  4. Comments on the Common Core mathematics 1st draft (K-5) « The Number Warrior Says:

    […] “lattice multiplication if you want to”, or any of the other methods. I am quite interested in what sort of drawing would explain the algorithm for long multiplication; […]

  5. Maria Droujkova Says:

    What a neat list!

    Check out Vedic multiplication. It’s similar to 5-10 finger method in nature, but uses a different notation structure.

  6. Angie Says:

    This is a great list… thanks for posting it!

  7. Dr Michael Taylor's Webpage Says:

    […] head in seconds. Some numbers you can multiply in seconds by criss-crossing lines. So far at least 25 different methods of multiplication have been identified. Maybe the list will be infinite – as many patterns as the mind can […]

  8. TwoPi Says:

    Maria: “Vedic multiplication” is in the first group (Procedures), under the names Crocetta and “vertically and crosswise” multiplication.

  9. Shyam Says:

    You don’t have this way…

  10. Ξ Says:

    Shyam, I think that’s the same as “Drawing Lines” [the last one under Procedures]. It’d be a challenge for large digits, but I think it’s really neat for small ones.

  11. pat ballew Says:

    Don’t know how many you are up to, but I failed to mention one that is used as a way of creating a Prime Sieve You can see an example here

  12. pat ballew Says:

    Sorry, entered too soon… This is just a type of nomograph that uses a parabola…There are lots of them for most every mathematical operation…

  13. Alexander Bogomolny Says:

    Egyptian multiplication is slightly different from Russian Peasants’:


  14. Ξ Says:

    Thanks Alexander (for this and your other multiplication links today)! My impression had been that there were two Egyptian methods, one of which was the same as what is called Russian multiplication, but I haven’t looked at the original sources. [I think there’s a copy of the Ahmes/Rhind Papyrus at one of the libraries in town, so once finals are done I ought to be able to verify one way or the other so that I can at least be accurate in my future teaching.]

  15. girl you don't now Says:

    how the heck did you come up with this stuff

  16. girl you don't now Says:

    you do know there are really 26 since you put 5 and a half

  17. Ξ Says:

    I think that there are probably more than this, since there are a lot of places where we don’t know how the people used to multiply. This is one of my favorite topics. 🙂

  18. Gaurav Tiwari Says:

    I would like to add one more way to multiply: See here:@ http://wpgaurav.wordpress.com/2011/08/31/do-you-multiply-this-way/

  19. mokurai Says:

    I forgot to mention the Schönhage-Strassen algorithm for multiplying extremely large numbers using the Discrete Fourier Transform (DFT). Once a mathematical curiosity, it is now in widespread use on computers as part of the Great Internet Mersenne Prime search, which tests numbers of a specific form with millions of digits to see whether they are primes. It has found 13 Mersenne primes in 15 years.

    There are numerous other digital techniques for integers of 32, 64, or some other modest numbers of bits, and for floating point numbers in various sizes, including many implemented on integrated circuits in signal processors and microprocessors. Some can be found in various computer design textbooks, such as Digital Systems: Hardware Organization and Design, by Frederick J. Hill and Gerald R. Peterson.

    Representing integers in forms other than decimal notation permits many other methods. For example, integers represented by their prime factors can be multiplied just by counting up how many of each prime factor there are in each number to be multiplied. As a trivial example, 32 is 2⁵, and 64 is 2⁶, so their product is 2¹¹. This representation makes addition much more difficult, however.

    Several methods, such as Egyptian and Russian peasant multiplication, are essentially equivalent to various forms of multiplication for binary numbers.

  20. Ξ Says:

    Gaurav, I think that’s the same as Crocetta, which is already in the list — I liked how you color coded the lines in a single pattern, though.

    mokurai, I’ve wondered about whether or not to include multiplication in different bases as each being different. It is in a way, though, and I’ll look at the book you mentioned — thanks!

  21. Megan R. Elkins Says:

    Thanks a lot for this quite a long list of very useful links! They really helped me today in my work.

  22. Chris R. Says:

    I suggest you do a Google search on “geometric compass Galileo”
    I think it overlaps here with a couple methods above but I think it should be mentioned somewhere in the list.

  23. Chris R. Says:

    I just wanted to add that the geometric compass of Galileo is also known under English Sector or French Sector like this:

  24. Garimella Swamy Prasad Says:

    very nice

  25. Nash Says:

    I am trying to find the name and book of a Naval architect who was throw in concentration camp in WW 2 who devised and later on wrote the book on alternate method of calculations the technique could beat a calculator. Can someone help.

    • Bob Mc Says:

      I read about this method (and the person who came up with it) in the 1950s while in a barbershop waiting for my haircut. Have thought about it frequently in recent years as the math-teaching discussion continues.

  26. boy Says:

    Thanks for posting it was really helpful but do you have the chinise method

  27. Ξ Says:

    I don’t think so, boy, unless you mean on an abacus. What method are you thinking of?

  28. daniela Says:

    Well I m really confused with all those methods , what I m looking for , if some one can help , is ..another 5 methods NOT given in the 25 list….. Anyone please ????? Thanks

  29. Why study the history of Mathematics Education? The case of multiplication. | Ravings of A Lunatic: Sense-Making in a Complex Field Says:

    […] https://threesixty360.wordpress.com/25-ways-to-multiply/ […]

  30. Playful Math Carnival 144: Anniversary Edition – Denise Gaskins' Let's Play Math Says:

    […] In #9, Heather Lewis began to explore The First Bunch of Ways to Multiply. [You can find the whole list at 25+ Ways to Multiply.] […]

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