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To multiply \(237\) by \(324\) without using a calculator, you can set it out like this:

1. The first two lines of the calculation use the same procedure as that of above.
2. In the third line we are multiplying by \(300\) (three hundreds). As we are multiplying by hundreds both the tens and unit digit will always be zero.
3. In a similar procedure to above:- \(3 \times 7 = 21\) put the \(1\) in the hundreds column and carry the \(2\) to the thousands column.
4. \(3 \times 3 = 9\); add the carried \(2\) to get \(11\), put \(1\) in the thousands column and carry \(1\) to the tens of thousands column.
5. \(3 \times 2 = 6\) add the carried \(1\) to get \(7\) so put the \(7\) in the tens of thousands column.
6. Add \(948\) and \(4740\) and \(71100\).

Therefore \(237 \times 324 = 76788\)

\(5607 \times 3061 = 17163027\)