Top indexing radical 艹 - anchors 芬 in the world of plants and flowers, the source of fragrance. Heads almost all flora vocabulary: 花 (flower), 草 (grass), 茶 (tea), 苹 (apple), 蓝 (indigo). Without it, 分 alone just means 'divide' with no scent in sight.
Bottom 分 supplies the exact sound fēn. The 'dividing / spreading' image adds a faint hint of fragrance dispersing through the air. Same phonetic family is huge: 份 (portion), 纷 (numerous), 粉 (powder), 氛 (atmosphere) - all share the fēn rime.
