What is the intuitive idea behind this claim on the divisor function?

Question

I want to understand the claim $$ \lim_{X \to \infty} \frac{\#\{n \le X : d(n) \equiv 0 \mod m \}}{X} = 1, $$ where $m \in \mathbb{Z}^+$ is fixed and $d(n)$ is the divisor function. I think that it means if we pick a positive integer $n$ at random, then $d(n) \equiv 0 \mod m$ with probability $1$, but I want to understand why this is true from a intuitive perspective. Also a reference for a proof would be great.