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.

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.

We need to convert all the lengths in cm.

Length of first wire = 10 m 54 cm = 1054 cm

Length of second wire = 11 m 56 cm = 1156 cm

1054 = $$2\times\ 17\times\ 31$$

1156 = $$2\times\ 17\times\ 2\times\ 17$$

highest common factors of 1054 and 1156 are 17 and 2.

Here the maximum length of each piece is 'x'. 

So the maximum value of x = $$17\times2$$ = 34