Maybe 짜 is pure korean word. But its meaning is pretty well explained by Leftium. In most case it mean a thing or person. But the Thing is there is a word 子[자] that exactly means thing or person as well.
연산자[演算子][operator]=연산[operating/calculating]+자[thing] (in math)
인자[因子][factor/a thing that draws another phenomenon]=인[cause]+자[thing]
공자[孔子][Confucius]=공[deep & serious (internally)]+자[person]
The reason I'm saying this is that, 일자 is spoken like 일짜 for the rule of spelling. So somehow 짜 and 子, I guess, are relevent each other.
I have one more reason for my arguement. I think 8 out of ten korean can guess the meanings closely (I'm Korean) when 짜 is replaced with 子 in some casees above(괴짜, 진짜, 가짜, 퇴짜, 알짜) except for 공자.