* Syllabification: This refers to dividing a word into syllables, which are the units of pronunciation. For example, "cat" is one syllable, "dog" is one syllable, and "happy" is two syllables (hap-py).
* Morphemic analysis: This involves breaking a word down into its smallest meaningful units, called morphemes. For example, the word "unbreakable" can be divided into the morphemes "un-" (meaning "not"), "break" (meaning "to separate"), and "-able" (meaning "capable of being").
* Etymology: This is the study of word origins, and it often involves tracing a word back to its root meaning. For example, the word "television" comes from the Greek words "tele" (meaning "far") and "vision" (meaning "sight").
The term you are looking for likely depends on the context of how you are dividing the word.