  In this paper we are interested in examples of locally compact quantum groups
$(M,\Delta)$ such that both von Neumann algebras, $M$ and the dual $\hat{M}$,
are factors. There is a lot of known examples such that $(M,\hat{M})$ are
respectively of type $(\rm{I}\_{\infty},\rm{I}\_{\infty})$ but there is no
examples with factors of other types. We construct new examples of type
$(\rm{I}\_{\infty},\rm{II}\_{\infty})$, $(\rm{II}\_{\infty},\rm{II}\_{\infty})$
and $(\rm{III}\_{\lambda},\rm{III}\_{\lambda})$ for each $\lambda\in [0,1]$.
Also we show that there is no such example with $M$ or $\hat{M}$ a finite
factor.
