According to Jewish law, you are only Jewish if you have a Jewish-born mother, or if you convert.
So if your great great grandmother was Jewish, and she had a daughter (who was your great grandmother), and she had a daughter (who was your grandmother) and she had a daughter (who was your mother) then you would be Jewish. But your great great grandfather has nothing to do with it.
Even under Reform Jewish law, which recognizes you as Jewish if your father is Jewish, they would not recognize "patrilineal descent" past one generation (in other words, you're not Jewish if your father's father was Jewish).
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you are only Jewish if your birth-mother was Jewish, or you convert. grandparents are out of the question
but if you mother's mother's mother was Jewish you are also.
Hebrew is a language, not a nationality. You can learn to speak Hebrew, but you can't BE Hebrew.