Old English sife "sieve," from Proto-Germanic *sib (source also of Middle Dutch seve, Dutch zeef, Old High German sib, German Sieb), from PIE *seib- "to pour out, sieve, drip, trickle" (see soap (n.)). Related to sift. The Sieve of Eratosthenes (1803) is a contrivance for finding prime numbers. Sieve and shears formerly were used in divinations.
late 15c., from sieve (n.). Related: Sieved; sieving.