\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015d.00520}
\itemau{Sprows, David}
\itemti{A classroom note on: some fast alternatives to division.}
\itemso{Math. Comput. Educ. 49, No. 1, 64-66 (2015).}
\itemab
From the introduction: Most students are aware of the fact that a number $N$ is divisible by nine exactly when the sum of the digits of $N$ is a multiple of nine. This fact gives a shortcut that allows one to determine if nine is a divisor of $N$ without performing a division (for large numbers it may be necessary to apply this fact more than once). Far fewer students know that a similar shortcut applies to the number eleven. In this note we will consider various shortcuts that can be used to determine if a given value divides a number $N$. In most cases these techniques are significantly faster than division. For completeness this note will include some techniques that are fairly ``obvious", but others of these shortcuts should be new to most students. This number analysis may be of interest to college mathematics groups or motivated liberal arts students.
\itemrv{~}
\itemcc{F30 F60}
\itemut{modular arithmetic; divisibility; student activities; shortcut to division}
\itemli{}
\end