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A classroom note on: some fast alternatives to division. (English)
Math. Comput. Educ. 49, No. 1, 64-66 (2015).
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.
Classification: F30 F60