Amoebas reproduce bya process called "binary fission" (splitting) to produce two daughter amoebas. The nucleus however divide by mitosis. This starts when the becomes a sphere fringed with small pseudopodia, whcih are constantly withdrawn and reformed while the nucleus mitotically divides. Then as the nucleus moves apart the cell splits down the middle producing two daughter amoebas. This process lasts for about an hour.

An amoeba producing identical offspring(adapted from Biology-Campbell et. al.)