I have read the following sentence:
I took note of the telephone number.
However, Cambridge dictionary says that "to take note of something" means "to give attention to something, especially because it is important". Example: You should take careful note of what she tells you because she knows their strategy well.
1) Based on that definition, my understanding is that "to take note of a telephone number" means "to pay attention to a telephone number", not necessarily to write it down. Is that right or can it also mean the latter, depending on the context?
2) If I meant that I wrote the telephone number down, I know I could use "to write down". Could I also use "to make a note of a telephone number" and "to note a telephone number" ? AFAIK "to make a note of sth", "to note sth" and "to write down sth" are synonyms..