[Math Lair] Russian Peasant Multiplication

Math Lair Home > Topics > Russian Peasant Multiplication

Russian Peasant Multiplication is a method of multiplying two numbers together that requires you only to know how to multiply by two and divide by two. While it is called "Russian Peasant Multiplication," it has been used in many cultures, including in ancient Egypt. As well, some computer systems use a similar procedure to perform multiplication.

Here's an example of how you would multiply 298 × 141 using this method:

  1. Write down the two numbers to be multiplied, separated by a vertical line:
    298141
  2. Divide the number on the left hand side by 2, ignoring any remainder. Write that number below the original number. Continue to divide by 2 until you reach 1:
    298141
    149
    74
    37
    18
    9
    4
    2
    1
  3. Multiply the number on the right hand side by 2, ignoring any remainder. Write that number below the original number. Continue to multiply by 2 until you reach the bottom number on the left side of the page:
    298141
    149282
    74564
    371128
    182256
    94512
    49024
    218,048
    136,096
  4. Cross out all rows where the left hand side is even:
    298141
    149282
    74564
    371128
    182256
    94512
    49024
    218,048
    136,096
  5. Sum the remaining numbers in the right column:
    298141
    149282
    74564
    371128
    182256
    94512
    49024
    218,048
    136,096
    42,018

If you multiply 298 × 141 either longhand or on your calculator, you will find that it is equal to 42,018.

So, how does this work? To see why it works, convert the two numbers to binary and multiply them, first longhand and then using the Russian peasant method. You'll definitely learn something new. Doing this should make it clear why the method works, and will also give you some insight into computer arithmetic.