Origin of Hangul
Ledyard holds that the Koreans adopted five core consonant letters from ’Phags-pa, namely ㄱ "g" , ㄷ "d" , ㅂ "b" , ㅈ "j" , and ㄹ "l" . These were the consonants basic to Chinese phonology, rather than the graphically simplest letters (ㄱ "g" , ㄴ "n" , ㅁ "m" , and ㅅ "s" ) taken as the starting point by the "Haerye." A sixth letter, the null initial ㅇ, was invented by Sejong. The rest of the consonants were developed through featural derivation from these six, essentially as described in the "Haerye"; a resemblance to speech organs was an additional motivating factor in selecting the shapes of both the basic letters and their derivatives.
Chinese family of scripts
The Hangul alphabet introduced in the 15th century was much simpler, and specifically designed for the sounds of Korean.
The alphabet makes systematic use of modifiers corresponding to features of Korean sounds.
Although Hangul is unrelated to Chinese characters, its letters are written in syllabic blocks that can be interspersed with Hanja. 
Such a Korean mixed script became the usual way of writing the language, with roots of Chinese origin denoted by Hanja and all other elements rendered in Hangul. Hanja is still used (but not very commonly like the Japanese) and is required in both North and South Korea.