You misunderstand 分 here.

分 does not mean "division" here. Here 分 means the "points" (test score), in an exam or a contest where the perfect score is 10.

> 三分  3 points (out of 10)
>
> 五分  5 points (out of 10)
>
> 十分 ①[original meaning] 10 points (out of 10), perfect score, full marks ②[extended meaning] "perfectly", very, extremely
>
> 幾分  how many points (out of 10)

Assuming that there is an exam called "love", how many points can I get from the exam?

>我愛你有幾分？
>
> How many points do I love you?
>
> How deep do I love you?


Extra examples:

> 三分天注定，七分靠打拼。 [famous lyrics]
>
> Three points depend on fate, while seven points depend on hardworking.
>
> [Chinese version of "nature versus nurture"]