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?