c. 1200, scouren, "cleanse by hard rubbing," probably via Middle Dutch scuren, schuren "to polish, to clean," and from Old French escurer, both from Late Latin excurare (Medieval Latin scurare) "clean off," literally "take good care of," from Latin ex "out," or here perhaps intensive (see ex-), + curare "care for, take care of" (see cure (v.)). OED suggests it entered the language as a technical term among Flemish workmen in England. From 1580s as "to wash vigorously." Related: Scoured; scouring. As a noun, 1610s, from the verb.
[move quickly in search of something], c. 1300, scouren, a word of uncertain origin, probably from Old Norse skyra "rush in," related to skur "storm, shower, shower of missiles" (see shower (n.)). This was likely influenced by or blended with Old French escorre "to run out," from Latin excurrere (see excursion).
The sense also probably has been influenced by scour (v.1) "cleanse by hard rubbing" and entangled with it in some figurative uses and in phrases such as scour the countryside "clear (a place) of enemies or undesirable persons." Middle English also had it as a noun, as in the expression in good scour "quickly, with all haste" (c. 1300).