Hasse diagram of the divisors of 30

Statement

Draw the Hasse diagram of the divisors of $30$ with the relation “divides”.

Solution

The divisors of $30$ are $1,2,3,5,6,10,15,30$. They are arranged on four levels (by number of prime factors) and two elements are joined only if one covers the other:

It is the “cube” of the subsets of $\{2,3,5\}$: each divisor corresponds to a subset of the prime factors.

Links

Topics: Set theory
Concepts: Hasse diagram · Partial order
Skills: Drawing a graph
Exercise type: Geometric problem