  An $n$-vertex graph is said to to be $(p,\beta)$-bijumbled if for any vertex
sets $A,B\subseteq V(G)$, we have \[e(A,B)=p|A||B|\pm \beta \sqrt{|A||B|}.\]
  We prove that for any $3\leq r\in \mathbb{N}$ and $c>0$ there exists an
$\varepsilon>0$ such that any $n$-vertex $(p,\beta)$-bijumbled graph with $n\in
r \mathbb{N}$, $\delta(G)\geq cpn$ and $\beta \leq \varepsilon p^{r-1}n$,
contains a $K_r$-factor. This implies a corresponding result for the stronger
pseudorandom notion of $(n,d,\lambda)$-graphs.
  For the case of triangle factors, that is when $r=3$, this result resolves a
conjecture of Krivelevich, Sudakov and Szab\'o from 2004 and it is tight due to
a pseudorandom triangle-free construction of Alon. In fact, in this case even
more is true: as a corollary to this result and a result of Han, Kohayakawa,
Person and the author, we can conclude that the same condition of
$\beta=o(p^2n)$ actually guarantees that a $(p,\beta)$-bijumbled graph $G$
contains every graph on $n$ vertices with maximum degree at most 2.
