c. 1300, preiere, "earnest request, entreaty, petition," also "the practice of praying or of communing with God," from Old French prier "prayer, petition, request" (12c., Modern French prière), from Medieval Latin precaria "petition, prayer," noun use of Latin adjective precaria, fem. of precarius "obtained by prayer, given as a favor," from precari "to ask, beg, pray" (from PIE root *prek- "to ask, entreat").
From mid-14c. as "devout petition to God or a god or other object of worship;" also "the Lord's Prayer;" also "action or practice of praying." Related: Prayers. Prayer-book "book of forms for public or private devotions" is attested from 1590s; prayer-meeting "service devoted to prayer, sacred song, and other religious exercises" is from 1780. Prayer-rug "small carpet spread and used by a Muslim when engaged in devotions" is by 1898 (prayer-carpet is by 1861). To not have a prayer "have no chance" is from 1941.
-ful
word-forming element attached to nouns (and in modern English to verb stems) and meaning "full of, having, characterized by," also "amount or volume contained" (handful, bellyful); from Old English -full, -ful, which is full (adj.) become a suffix by being coalesced with a preceding noun, but originally a separate word. Cognate with German -voll, Old Norse -fullr, Danish -fuld. Most English -ful adjectives at one time or another had both passive ("full of x") and active ("causing x; full of occasion for x") senses.
It is rare in Old English and Middle English, where full was much more commonly attached at the head of a word (for example Old English fulbrecan "to violate," fulslean "to kill outright," fulripod "mature;" Middle English had ful-comen "attain (a state), realize (a truth)," ful-lasting "durability," ful-thriven "complete, perfect," etc.).