Remainder Graphs

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)

.