Divisors of a natural number

Definition

Let $n$ be a positive integer. The set of divisors of $n$ is the set of positive integers $d$ that divide $n$: $$D(n) = \{ d \in \mathbb{Z}_{>0} : d \mid n \}.$$

Remarks

The set $D(n)$ is finite, because each $d \in D(n)$ satisfies $1 \le d \le n$. It always contains $1$ and $n$. For example, $D(12) = \{1, 2, 3, 4, 6, 12\}$. The map $d \mapsto n/d$ is a bijection from $D(n)$ to itself. Sums over $D(n)$ define the divisor function and the Dirichlet convolution.

Explanations

L1 human

The divisors of $n$ are the numbers that go into $n$ with no remainder. They come in pairs $d$ and $n/d$. For $n = 12$, the pairs are $1$ and $12$, $2$ and $6$, and $3$ and $4$.