Remainder Graphs

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What is the remainder when some number is divided by another number, for example, 7? The result is called . You can find the answer quickly with the help of one of the graphs in this Demonstration.


For a number, say , select the desired modulus, then start at 0 and follow 9 blue arrows, 1 red arrow, 4 blue arrows, 1 red arrow, 0 blue arrows, 1 red arrow, then 6 blue arrows. If there is no red arrow, stay in place. Each digit specifies the number of blue arrows, then follow a single red arrow before moving on to the next digit. The number on your final landing place gives the remainder. In this example, .


Contributed by: Ed Pegg Jr (November 2015)
Open content licensed under CC BY-NC-SA




[1] D. Wilson, "Divisibility by 7 Is a Walk on a Graph," Tanya Khovanova's Math Blog (blog, T. Khovanova, owner), (Aug 11, 2009)

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