# A problem from RMO 2004

**Number Theory**Level 4

Positive integers are written on the six faces of a cube. On each corner of the cube the products of the numbers written on the faces which meet at that vertex is written. The sum of the numbers written on all the vertices of cube is 2004. If \(T\) denotes the sum of the numbers written on the faces of the cube, which of the following is a possible value of \(T\)?