Explanation:

- Check divisibility by 4: A number is divisible by 4 if its last two digits form a number divisible by 4. Here, '16' is divisible by 4.

- Option 1: 4 (Correct Answer)

- Check divisibility by 5: A number is divisible by 5 if it ends in 0 or 5. 5769116 ends in 6, so it isn't divisible by 5.

- Option 2: 5

- Check divisibility by 8: A number is divisible by 8 if its last three digits form a number divisible by 8. Here, '116' is not divisible by 8.

- Option 3: 8

- Check divisibility by 12: A number is divisible by 12 if divisible by both 3 and 4. Sum of digits is 35, not divisible by 3.

- Option 4: 12