Recall the diatonic scale formula of TTSTTTS. A tetrachord is TTS. A diatonic scale is two tetrachords separated by a tone.
|Lower TetrachordXX||Upper TetrachordXX|
The same tetrachord will do for two diatonic scales.
The lower tetrachord of C is the upper tetrachord of F. The diatonic scale of F concludes in the same way the diatonic scale of C begins, CDEF.
The upper tetrachord of C is the lower tetrachord of G. The diatonic scale of G begins in the same way the diatonic scale of C ends, GABC.