Animated Remainder Graph

modulus

7

input integer

169

algorithm step

1

A remainder graph provides a visual way to calculate the remainder

n(modm)

upon dividing a given integer

n

by a given modulus

m

. To find the value of the remainder, take a walk on the graph starting at the 0 node. Read off the digits of

n

from left to right. For each digit, walk the same number of steps along the black arrows, followed by a single step along a blue arrow. Continue until you follow the black arrows for the final digit. The node you end up at is the value of

n(modm)

.

This Demonstration displays the remainder graphs for various choices of modulus. Given a positive integer, it also provides an animation of the process of walking along the graph.