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The Russian Multiplication Method


Russian peasants, according to some mathematicians, used a curious process of multiplication.

Let's look at an example, where we will get the product from number 36 by number 13.

We write the two factors (36 and 13), side by side:
36 --------- 13

We determine half of the first and double of the second by writing the results below the corresponding factors:
36 -------- 13
18 -------- 26

We proceed in the same way with the obtained results:
36 --------13
18 -------- 26
9 --------- 52

Again, we repeat the operation. As we get to an odd number (which in this case is 9), we must subtract one unit and take half of the result. From 9, subtracting 1 we get 8, half of which is 4. We proceed this way until we reach the term equal to 1 in the left column.
We have therefore:
36 ------- 13
18 ------- 26
9 ----- 52 (X)
4 ------ 104
2 -------208
1 --- 416 (X)

Summing the numbers in the right column that correspond to the odd numbers in the left column (ie the ones we mark with an X), we get:
52 + 416 = 468

The result obtained (468) will be the product of the number 36 by 13.