Why did Old English use C while other Germanic languages used K?
During most the first millennium CE, North and West Germanic languages were written in runic alphabets. Gradually, each language shifted from the runic alphabet to the Latin alphabet. The people who adapted the Latin alphabet for use with a new language chose which letters to align with which sounds. For the phoneme /k/, the Latin alphabet offered two choices: C and K. In most cases K was chosen, and to this day German, Dutch, and the Scandinavian languages make very sparing use of C, except in digraphs like CH. But for Old English, they opted for C, and in fact K is not even included in the Old English Latin alphabet. Why the difference?
--EDIT--
After some answers and a bit more research, it is clear that Old English used C, following the practice of the Insular Celtic languages, which followed the practice of Latin. So the question becomes: Why did the other Germanic languages use K? Why did they adopt the Latin alphabet but not the Latin practice of using C?
--EDIT--
After some more research, it seems that the most likely answer is the time in which these languages adopted the Latin alphabet, specifically, before or after the palatalization of /k/ and /g/ in Vulgar Latin. When the Celtic scribes learned the Latin alphabet, it was from Romans, so they based their letter choices on Latin. Later, in the Romance languages derived from Vulgar Latin, C could refer to either /k/ or a palatalized version like /tʃ/, while K was unchanged. Since these languages, such as Old French, were widespread at the time, the people adapting the Latin alphabet for continental Germanic languages saw C as an unneeded complexity and opted for the simpler option, K.
This is speculation on my part so if anybody has more definite information, it would be appreciated.
*The letter K comes from the Greek letter Κ (kappa), which was taken from the Semitic kap, the symbol for an open hand.' This, in turn, was likely adapted by Semites who had lived in Egypt from the hieroglyph for "hand" representing D in the Egyptian word for hand, d-r-t. The Semites evidently assigned it the sound value /k/ instead, because their word for hand started with that sound.
In the earliest Latin inscriptions, the letters C, K and Q were all used to represent the sounds /k/ and /g/ (which were not differentiated in writing). Of these, Q was used to represent /k/ or /g/ before a rounded vowel, K before /a/, and C elsewhere. Later, the use of C and its variant G replaced most usages of K and Q. K survived only in a few fossilized forms such as Kalendae, "the calends".
When Greek words were taken into Latin, the Kappa was transliterated as a C. Loanwords from other alphabets with the sound /k/ were also transliterated with C. Hence, the Romance languages generally use C and have K only in later loanwords from other language groups.
The Celtic languages also tended to use C instead of K, and this influence carried over into Old English.
(Wikipedia)
I have read that until the time of grammarian guru, Quintilian ( 1st century AD.) "c" and "k" were both used in Latin. However, Quintilian put it about that "k" was not to be used, only "c". Therefore, the Romance languages, descended from Latin, hardly ever use 'k".
High German was not really developed until Luther's time and afterwards, when Greek was part of classical education. German academia having, broken away from the Roman church were reading old Christian documents in Greek, and perhaps decided that the more ancient "k" usage in their "newer" language gave it some cachet.
The really interesting "c" and "k" usage, is in Ireland, where there are many place names and surnames beginning with 'K". How to explain it.
While rarely mentioned in potted histories, Caesar apparently said that, while the Britons only spoke their own language, some could write in Greek. Possibly the same in Ireland, the Greeks being great sailors and mapmakers. There is also Kieran and Ciaran, of course. Also 'Kells" according to Bede is an alternative spelling of Cells.