id: 06443535
dt: j
an: 2015d.00520
au: Sprows, David
ti: A classroom note on: some fast alternatives to division.
so: Math. Comput. Educ. 49, No. 1, 64-66 (2015).
py: 2015
pu: MATYC Journal, Old Bethpage, NY
la: EN
cc: F30 F60
ut: modular arithmetic; divisibility; student activities; shortcut to division
ci:
li:
ab: 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
â€śobvious", 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.
rv: