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Peasant multiplication

Peasant multiplication is an old algorithm for multiplication. It requires no use of a multiplication table; however, it requires that the user be able to divide by 2. The user must also know how to add.

Example: 27 times 82
A-columnB-columnAdd this
278282
13164164
6328
3656656
113121312
Result: 2214

The method works because multiplication is distributive, so: 82 * 27 = 82 * (1*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 1*2^4) = 82 * (1 + 2 + 8 + 16) = (82 + 164 + 656 + 1312) = 2214.

This method was known to ancient Egyptians as mediation and duplation, where mediation means halving one number and duplation means doubling the other number. It is still used by peasants in some areas, such as Russia.

See also: Multiplication algorithm, Binary numeral system.

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