adjective ("pertaining to or indicating character") and noun ("a distinctive trait; that which gives or indicates character") both first attested 1660s, from character + -istic on model of Greek kharaktēristikos. Earlier in the adjectival sense was characteristical (1620s). Related: Characteristically (1640s). Characteristics "distinctive traits" also attested from 1660s.

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Definitions of characteristic from WordNet
characteristic (n.)
a prominent attribute or aspect of something;
generosity is one of his best characteristics
Synonyms: feature
characteristic (n.)
a distinguishing quality;
characteristic (n.)
the integer part (positive or negative) of the representation of a logarithm; in the expression log 643 = 2.808 the characteristic is 2;
characteristic (n.)
any measurable property of a device measured under closely specified conditions;
Synonyms: device characteristic
characteristic (adj.)
typical or distinctive;
heard my friend's characteristic laugh
red and gold are the characteristic colors of autumn
stripes characteristic of the zebra