Several parts combine into one character.

The traditional 腦 is a compound: 月 (flesh) + 𡿺 (a striking pictograph of an infant's skull with the soft fontanelle on top, hair growing through it). The original etymology was anatomically precise: the brain sits in the skull where a baby's soft spot is, where hair grows. The character documented exactly where this organ resides in the body. Japan simplified to 脳, Mainland China to 脑 — both replaced the elaborate 𡿺 with a simpler shape, but kept the core 月 (flesh) radical that anchors body-part characters.

Korean reading "noe." 頭腦 (dunoe, "head-brain" = brain / intellect — used in both anatomical and intellectual senses), 腦炎 (noeyeom, encephalitis), 腦死 (noesa, brain death — the legal definition central to Korean organ-donation policy), 腦電圖 (noejeondo, electroencephalogram), and the politically loaded 首腦 (sunoe, "head-brain" = head of state / leader — used for national leaders, as in 정상회담 vs 수뇌부 chief leadership).

Mandarin nǎo, 3rd tone (simplified 脑). 头脑 (tóunǎo, brain / mind — same compound structure as Korean 두뇌), 脑子 (nǎozi, brain — colloquial), 脑袋 (nǎodài, head — extremely casual). Most importantly, the modern Mandarin word for computer: 电脑 (diànnǎo, "electric brain") — a 1970s coinage that beautifully captures what a computer is. Compare to Japanese コンピューター (loanword) and Korean (loanword). Only Mandarin coined a native compound. By extension: 笔记本电脑 (bǐjìběn diànnǎo, notebook computer = laptop), 平板电脑 (píngbǎn diànnǎo, "flat-board electric brain" = tablet).

Japanese on-reading ノウ (nō) — 脳 (nō, brain), 頭脳 (zunō, brain / intellect), 脳波 (nōha, brain waves / EEG), 首脳 (shunō, head of state / leader — used identically to Korean), 脳裏 (nōri, "brain interior" = the back of one's mind, used in expressions like 脳裏に焼き付く "to be burned into one's memory"). 脳 has essentially no kun-reading; the on-reading nō dominates.

Memory aid: flesh (月) at the top of the body where the soft fontanelle and growing hair mark the position — the brain.