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If the two numbers each have N digits, that's N 2 (or N x N) multiplications altogether. In the example above, N is 3, and we had to do 3 2 = 9 multiplications.
For example, an algorithm to add three numbers can have two steps: add the first two numbers in the first step and the result to the third number in the second step.
Mathematicians have reportedly discovered a new way of multiplying two numbers together. The new technique is for really large numbers, and if it passes a peer-review, could be the fastest ...