Prime Factorization Graph

number

2

largest prime factor

outside

inside

Let

m

and

n

be distinct integers such that

m

divides

n

. Then the vertices of a polygon with

n

vertices can be connected to a polygon with

m

vertices from

n/m

equally spaced vertices on the first polygon. This procedure can be applied repeatedly to the prime factors of a number in order to get visualizations of the factorizations of the numbers. For instance,

15=3×5

can be seen as a polygon of 15 vertices connected to a triangle at every fifth vertex.