Learn Hardcore Chinese: qǐng jìzhù wǒ de shǒujīhào.

记 by itself means “to remember / to memorize / to note.”
住 here is a resultative complement meaning something like “firmly / successfully / and keep it that way.”

So:

记: the action of remembering.
记住: to successfully remember and retain it.

Compare:

你记我的名字了吗？ – Did you remember my name? (more general)
你记住我的名字了吗？ – Did you manage to remember (and keep in mind) my name?

In 请记住我的手机号, the speaker is asking you not just to try, but to successfully commit it to memory.

What exactly does 的 do in 我的手机号?

的 is a possessive/attributive particle that links the possessor to the thing possessed.

我 = I / me
的 = makes it “my”
手机号 = cellphone number

So:

我的手机号 = “my cellphone number”

Structure:

X 的 Y ≈ “X’s Y”
- 我的手机号 → my phone number
- 他的书 → his book
- 老师的车 → the teacher’s car

In standard, careful speech and writing, you should include 的 here.

Can I drop 的 and just say 我手机号?

In everyday spoken Mandarin, native speakers do sometimes drop 的 between pronouns and very common nouns:

我手机 (my phone)
我妈 (my mom)
我朋友 (my friend)

With 手机号, you might hear:

我手机号 in fast or casual speech.

However:

我的手机号 is the safe, standard form.
As a learner, it’s better to keep the 的. Dropping it is more of a native-speaker fluency thing and can sound wrong if overused or used in the wrong places.

What is 手机号 exactly? How is it different from 手机号码 or 电话号码?

手机 = mobile phone, cellphone
号 / 号码 = number

So:

手机号 is a colloquial abbreviation of 手机号码:
- 手机号 ≈ “cellphone number” (everyday speech)
- 手机号码 ≈ “cellphone number” (more complete, common in forms, writing)

电话号码 is more general:

电话 = phone (not specifically mobile)
电话号码 = “telephone number”, can be landline or mobile depending on context.

Summary:

手机号: very common, casual, specifically mobile number.
手机号码: full form, sounds a bit more formal/complete.
电话号码: any phone number (landline or mobile).

Can I say 请把我的手机号记住 instead? What’s the difference?

Yes, 请把我的手机号记住。 is also correct.

Differences:

Original sentence (no 把):
- 请记住我的手机号。
  Focuses on the action “remember” and then states what to remember.
With 把:
- 请把我的手机号记住。
  Uses the 把-construction, which highlights how the object (my phone number) is affected by the action:
- literally: “Please take my phone number and remember it.”

Nuance:

Both are natural.
The 把 version slightly emphasizes that you are doing something to “my phone number” (i.e., committing it to memory).
In everyday conversation, 请记住我的手机号 is a bit more straightforward and common for learners to use.

What’s the difference between 记住 and 记得? Could I say 请记得我的手机号?

Yes, 请记得我的手机号。 is grammatical and natural, but there’s a nuance difference:

记住: emphasizes the result of successfully remembering and holding it in memory.
记得: emphasizes the state of remembering (“to remember / to recall”).

Rough nuance:

请记住我的手机号。
→ “Please (manage to) remember my number and keep it in mind.”
请记得我的手机号。
→ “Please remember my number (don’t forget it).”

They often overlap and both are acceptable. 记住 tends to sound a bit more like memorize it firmly, while 记得 is slightly more about not forgetting.

Why is there no subject like 你 (“you”) in this sentence?

Mandarin often drops the subject in imperatives/commands when it is obvious from context.

请记住我的手机号。
Literally: “Please remember my cellphone number.”

If you include 你, it becomes:

请你记住我的手机号。
→ “Please (you) remember my cellphone number.”

Both are correct. The version without 你 is very typical and sounds natural, just like English often omits “you” in commands (“Please sit down.”).

Do I need a measure word (classifier) with 手机号 here?

Not in this sentence.

手机号 is used here as a specific known thing (“my cellphone number”), so no measure word is needed:
- 我的手机号 = my cellphone number

You would use a measure word if you talk about how many numbers or one of them:

一个手机号 – one cellphone number
三个手机号 – three cellphone numbers

But when you say “my phone number” as a specific item, 我的手机号 is perfectly natural without a measure word.

How should I pronounce this sentence, especially the tones? Is there any tone sandhi?

Character + pinyin + tone:

请 qǐng – 3rd tone (dips, but in connected speech it often sounds like 2nd tone before another 3rd)
记 jì – 4th tone (falling)
住 zhù – 4th tone
我 wǒ – 3rd tone
的 de – neutral tone
手 shǒu – 3rd tone
机 jī – 1st tone
号 hào – 4th tone

Tone sandhi to note:

请 (3rd) + 记 (4th): the 3rd tone on 请 is usually pronounced like a 2nd tone in fast speech → sounds like “qíng jì…”
手 (3rd) + 机 (1st): 3rd + 1st is pronounced normally: shǒu jī.

So in natural speech, you’ll often hear something close to:

qíng jì zhù wǒ de shǒu jī hào
(with 请 sounding like 2nd tone due to 3rd-tone sandhi).

Could I say just 请记住我的手机? Would that mean the same thing?

No, that would change the meaning.

手机 = mobile phone (the device)
手机号 / 手机号码 = mobile phone number

So:

请记住我的手机。
Literally: “Please remember my cell phone.” (the physical phone, which is odd)
请记住我的手机号。
“Please remember my cellphone number.” (what you dial)

To talk about the number, you must use 号 / 号码.

How formal or polite is 请记住我的手机号? Would it sound rude?

Adding 请 already makes it polite.
But the structure is still a direct request (“Please remember …”).

In different contexts:

To a friend: totally fine, may sound a bit serious; many people would just say:
- 记住我的手机号啊。 (casual)
To be extra polite/soft (e.g., to a client or teacher), people often use phrases like:
- 麻烦你记一下我的手机号。
  (“Could I trouble you to take note of my phone number?”)
- 请您记一下我的手机号。 (using 您, polite “you”)

So 请记住我的手机号。 is polite enough in most everyday situations and not rude, but it’s still relatively direct.

How would I turn this into a question like “Can you remember my phone number?” in Chinese?

You can use 能 or 可以 and/or add 吗:

Ability / possibility:
- 你能记住我的手机号吗？
  → “Can you remember my cellphone number?”
- 你可以记住我的手机号吗？
  → “Can you (are you able to) remember my cellphone number?”
About whether you have already remembered it:
- 你记住我的手机号了吗？
  → “Have you remembered my cellphone number?”

All of these are natural; choose depending on whether you’re asking about ability or whether they have already memorized it.