What traits do archaeans and bacteria share?

These are both  microscopic, unicellular organisms of no cell organelles; that is they lack the basic organelles of cells like the mitochondria, endoplasmic reticulum, nucleus etc.Their genetic materials are conserved in a single circular chromosomes, unlike in eukaryotes where they are packed   in nucleus. Other similarities are:

Both  are Prokaryotes.

They both lack nucleus

They both lack membrane bound organelles.

They both undergo reproduce asexually by  binary fission.

Both also have plasma membranes.

Explanation:

i would say the prokaryotic cells the prokaryotic cells are less complex, are usually found only in unicellular organisms and have more limited capabilities than eukaryotic cells.