A New Method to divide Numbers by 8 (Eight)!

Consider the following procedure for dividing the three-digit number \(375\) by \(8\):

  • Write down the number formed by the first two digits, namely \(37\).

  • Multiply this by \(2\) to get \(74\).

  • Add to this, the units digit of \(375\) (the original number), obtaining \(74+5=79\).

  • Then divide it by \(8\) to get \(9\) with a remainder of \(7\).

  • Add this result (\(9\), remainder \(7\)) with \(37\) (the first two digits of the original number) to get your answer: \(46\), remainder \(7\).

Thus \(375\) divided by \(8\) equals \(46\) with a remainder of \(7\).

Does this method always work for three-digit numbers? Why, or why not?

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