Two wires of lengths 10 m 54 cm and 11 m 56 cm are both cut into pieces of length x cm each, where x is an integer. Find the maximum value of x.

42 56 34 28

34

Length of first wire = 10 m 54 cm = 1054 cm Length of second wire = 11 m 56 cm = 1156 cm 1054 = 2 × 17 × 31 1156 = 2 × 17 × 2 × 17 highest common factors of 1054 and 1156 are 17 and 2. So the maximum value of x = 2 × 17 = 34