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Remainder Graphs

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modulus
7
What is the remainder when some number
n
is divided by another number, for example, 7? The result is called
n(mod7)
. You can find the answer quickly with the help of one of the graphs in this Demonstration.
For a number, say
n=9406
, 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,
9406=5(mod7)
.
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