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: