The hexadecimal representation of 6578 is

Key idea: convert the octal number to a form that maps easily to hexadecimal (either via binary grouping or via decimal conversion).

1. Convert each octal digit to 3-bit binary: 6 → 110, 5 → 101, 7 → 111.

2. Concatenate the binary groups: 110101111. Pad on the left so the total length is a multiple of 4: 0001 1010 1111.

3. Convert each 4-bit group to hexadecimal: 0001 → 1, 1010 → A, 1111 → F. So the hexadecimal representation is 1AF.

Alternate method (octal → decimal → hex):

1. Compute the decimal value: 6*8^2 + 5*8^1 + 7*8^0 = 6*64 + 5*8 + 7 = 384 + 40 + 7 = 431.

2. Convert 431 to hexadecimal by repeated division: 431 ÷ 16 = 26 remainder 15 (F); 26 ÷ 16 = 1 remainder 10 (A); 1 ÷ 16 = 0 remainder 1. Reading remainders up gives 1AF.

Final answer: 1AF