Pòl is looking for the Pink Girls phone numbers. They gave him the number for the speaking clock. :)
Without any additional contextual information a phone number is probably the most likely meaning, although others are certainly possible, as in English.
However, there is an English idiom 'to have someone's number' that means to understand someone's real motives and thereby gain some advantage, and I doubt that the Irish could include this meaning.
Social security number? Passport number? Bank account number? My age? What number are you talking about?