各 + measure, 各 X 各 Y, and 互相 + V — distributive and reciprocal patterns
Three closely related patterns. (1) 各 + measure / classifier / noun = 'each / every': 各位 = everyone (formal), 各种 = each kind, 各国 = each country, 各地 = each place, 各人 = each person. The 各 picks out the members one by one. (2) 各 X 各 Y (often 各 V 各的) = 'each does their own X and Y' — separation / non-coordination: 各做各的 = each doing their own (thing), 各走各的路 = each walks their own path. (3) 互相 + V = 'mutually V / V each other': 互相帮助 = help each other, 互相尊重 = respect each other. 各 distributes; 互相 binds reciprocally. They're often the literal opposite of each other — 各 separates, 互相 unites — and learners need both for everything from polite address (各位) to relationship advice (互相理解).
各 + measure / classifier — picking each one out
各 gè = 'each / every'. Unlike 每 (every / each one), 各 typically attaches to a measure, classifier, or noun directly without a number. 各位 = everyone (literally 'each position') — used for polite address: 各位老师 = teachers (everyone), 各位同学 = students (everyone), 各位先生女士 = ladies and gentlemen. 各种 = each kind / various: 各种水果 = various fruits, 各种问题 = various problems. 各国 = each country / various countries: 各国领导人 = leaders of various countries. 各地 = each place / everywhere: 来自各地 = from various places. 各人 = each person: 各人有各人的看法 = each person has their own view. 各方面 = each aspect / every aspect: 各方面都很好 = good in every respect. 各家 = each household / family: 各家有各家的难处 = each family has its own difficulties (a famous proverb). The 各 is more formal / written than the everyday 每 + measure + noun (e.g. 每个人 = each person), and it lends a slightly elevated, sometimes ceremonial flavor.
各 vs. 每 — distinction in flavor
各 and 每 both translate 'each / every' but differ. 每 is more concrete / quantitative: 每个学生都有一本书 = every student has a book (counts each one). 各 is more distributive / categorical: 各个学生都有自己的问题 = each (kind/category of) student has their own problems. Often interchangeable, but: 每 prefers 每 + 个 / 天 / 年 + noun (each + measure + noun). 各 prefers 各 + noun-classifier without 个 (各位, 各种, 各国, 各地). You DO see 各个 (= each individual one), which is acceptable: 各个国家都有自己的文化 = each country has its own culture. Usage rules of thumb: for polite address use 各 (各位); for counting / iterating use 每 (每天 = every day); for variety / categories use 各 (各种 = various kinds). 每天 ✓, 各天 ✗ (各 doesn't work here). 各国 ✓ is more idiomatic than 每国 for 'various countries'. Read enough news and you'll feel the difference.
各 X 各 Y — 'each does their own X and Y'
各 X 各 Y is a distinctive pattern meaning 'each does their own X / Y' — emphasizing SEPARATION rather than coordination. The classic frame: 各 + V + 各的 (+ N) = 'each V's their own (N)'. 各做各的 = each does their own (thing). 各走各的路 = each walks their own path. 各唱各的歌 = each sings their own song. 各管各的 = each minds their own (business). 各想各的办法 = each thinks of their own solution. 的 at the end nominalizes 'their own (one)'. The pattern strongly suggests independence / non-cooperation. 我们各做各的吧。 = Let's each do our own thing. 他们各走各的路了。 = They each went their own way (often used for breakups or partnerships ending). A: 你们一起做这个项目吗? B: 不,各做各的。 = A: Are you doing this project together? B: No, each doing our own. The flavor: 'no need to coordinate / let's not interfere with each other / we're going separate ways'. Sometimes neutral ('we each take care of our own slice'), sometimes mildly tense ('we're done collaborating'). Context decides.
各 X 各的 vs. 各自 — 'each on their own / respectively'
Closely related is 各自 gèzì = 'each / respectively / on one's own'. 他们各自有自己的家。 = They each have their own home. 请大家各自完成作业。 = Please everyone complete the homework on your own / respectively. 我们各自买票。 = We each buy our own tickets (separately). 各自 is a more written / careful form than 各 X 各的, but both express the same distributive-with-independence flavor. Compared to 各: 各自 is a fuller adverb / pronoun ('each + self'), while 各 alone is more bound (needs to attach to a noun / measure / verb). Use 各自 when you want to say 'each on their own' as a complete adverbial. Use 各 X 各的 when you want to emphasize the independence of action ('each does their own'). They're cousins; native speakers reach for whichever sounds natural: 大家各自回家 = everyone went home separately, vs. 大家各回各家 = each goes to their own home (more idiomatic / playful).
互相 + V — 'mutually V / V each other'
互相 hùxiāng is the dedicated reciprocal adverb: 'mutually / each other'. 互相 + V = V each other / mutually V. 互相帮助 = help each other. 互相尊重 = respect each other. 互相理解 = understand each other. 互相支持 = support each other. 互相学习 = learn from each other. 我们应该互相帮助。 = We should help each other. 朋友之间要互相理解。 = Between friends (we) need to understand each other. The pattern works with most relationship verbs: 爱, 信任, 关心, 鼓励, 介绍, 联系, 影响. Note: 互相 typically pairs with TWO-CHARACTER verbs. Single-character verbs sound off: 互相帮 is awkward; 互相帮助 is fine. For single-character verbs use 彼此 bǐcǐ + V or rephrase. 互相 doesn't take an object the way English 'each other' does — the verb itself absorbs the reciprocal meaning. NOT 他们互相爱对方 (redundant); just 他们互相爱 or better 他们相爱 (the prefix 相 is the bound classical reciprocal). 相爱 = love each other, 相识 = know each other, 相信 = believe / trust each other (this last one has drifted to mean 'believe' generally). 互相 is the productive modern equivalent.
彼此 / 相互 / 相 — register variants
Reciprocity has several flavors in Mandarin. 互相 is the standard, most common form. 相互 xiānghù is virtually identical, slightly more formal / written: 相互理解 = mutual understanding (often as noun phrase). 彼此 bǐcǐ = 'each other / one another' — can stand alone as a pronoun-like adverb: 彼此尊重 = respect each other, 我们彼此都很了解 = we know each other very well. 彼此 is slightly more formal and works with single-character verbs better: 彼此关心 = care for each other. 相 + V is the bound classical prefix: 相爱 (love each other), 相识 (know each other), 相处 (get along), 相反 (opposite), 相同 (same), 相似 (similar), 相比 (comparing). Many fixed compounds. Reading order from frequency: 互相 > 彼此 ≈ 相互 > bound 相. Pick the one matching register: speech / general writing → 互相; careful writing / nominal phrase → 相互; with single-char verb or stand-alone → 彼此; in fixed compounds → 相.
Common patterns and traps
Trap 1: using 各 with a number. 各两个 is wrong; you'd say 每两个 (every two) or rephrase. 各 doesn't take numbers. Trap 2: forgetting 的 in 各 X 各的. 各做各 is incomplete; the canonical pattern is 各做各的 (their own). The 的 is essential. Trap 3: 互相 with single-character verb. 互相帮 is awkward; needs 互相 + 2-syllable verb (互相帮助). For single-char verbs use 彼此 or rephrase. Trap 4: redundant object after 互相. 他们互相爱对方 is wrong (互相 already means 'each other'). Just 他们互相爱 or 他们相爱. Trap 5: confusing 各 (each, distributive) with 都 (all, universal). 各人都有自己的看法 = each person has their own view (distributive — emphasizes individual variety). 大家都很好 = everyone is fine (universal — uniform). Different grammatical roles. Trap 6: using 各 in casual speech where 每 is more natural. 各位 in formal address is fine, but for everyday 'every day' / 'every person' use 每天 / 每个人. 各 has a slightly elevated register. Trap 7: 各自 vs. 各 X 各的. Both express 'each on their own'. 各自 is a single adverb / pronoun, 各 X 各的 is a verb-phrase pattern. Don't blend them: 各自做各的 is awkward; pick one frame.
