Zahl is used when it's not associated with anything, such as math. Nummer is used when the number means something. EG 'He lives in apartment number 5', here you would used Nummer. 'What number is 3 plus 5?' here you would use Zahl.
Can't it be "Seven is your number" as well? If used in formal form. I guess the only thing that hints to "her" is the lowercase "ihre", I guess it should be "Ihre" for formal "your". However, I feel that "your number" should be accepted as well.