2021 AMC 12D Question 12

For $n$ a positive integer, let $f(n)$ be the quotient obtained when the sum of all positive divisors of $n$ is divided by $n.$ For example, $$
\begin{aligned} f(14) &= (1 + 2 + 7 + 14) \div 14 \\ &= \dfrac{12}{7}. \end{aligned}
$$ What is $f(768) - f(384)?$