What number can divede 17 ,51 ,34

• Factors of 17: $1, 17$
• Factors of 51: $1, 3, 17, 51$ (since $51 = 3 \times 17$)
• Factors of 34: $1, 2, 17, 34$ (since $34 = 2 \times 17$)

The common factors are 1 and 17.

The greatest number that can divide 17, 51, and 34 is 17.