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- Waitâperhaps the number is divisible by **each** of 7, 11, and 13âmeaning divisible by their **product**, so $ z $ must be a multiple of 1001. The smallest such $ z $ is 1001, but it is not three-digit.
- Therefore, **no** three-digit number satisfies this.
- But this cannot beâlikely an error in assumption.
- Unless the number is not required to be divisible by the product, but by **some**âbut no.
- Alternatively, perhaps the problem meant: divisible by **one** of them, but says âandââhighlighting shared constraint.
- Given the difficulty, reconsider: maybe the number is divisible by **each** 7, 11, 13âso must be multiple of 1001.
