Congruence ≡

Numbers are congruent when they have the same remainder after being divided by a chosen whole number (called the modulus).

Example: 2 and 14 with a modulus of 12

212 = 0 with a remainder of 2

1412 = 1 with a remainder of 2

They have the same remainder,
so 2 and 14 are congruent (modulus 12)

So they are congruent when, after spinning around any number of times, they land together.

Play with it here:

Another Way of Looking at It

We can also subtract the numbers and see if the result is a multiple of the modulus.

Example: 2 and 14 mod 12 (again)

14 − 2 = 12
12 / 12 = 1 exactly