# Number of operations in grade school algorithm for multiplying 577 and 423

Given 577 x 423 with grade school algorithm you calculate

577 x 3 = 1731

577 x 2 = 1154

577 x 4 = 2308

These are 3 multiplications of a number by a single digit.

Then, you go on and add

1731 + 11540 = 13271

and then

13271 + 230800 = 244071 to get the result

At the bottom line, this makes ~ 5 operations (of course depending on the number of digits you take, e.g., if you conceive the whole operation, it is just one multiplication, but this set aside).

In my copy of CC by Arora and Barak (you can have a look at page xx) it says for this "3 multiplications of a number by a single digit and 3 additions". Is this an error? Thank you.

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Note also that the $243071$ in Figure 1 should be $244071 \,(=423 \cdot 577)$. – Shai Covo Jul 13 '11 at 10:54