Question 24
The six-digit number $\overline{ABCDEF}$ uses each digit 1, 2, 3, 4, 5, 6 exactly once. The prefixes $\overline{AB},\overline{ABC},\overline{ABCD},\overline{ABCDE},\overline{ABCDEF}$ are divisible by 2, 3, 4, 5, 6 respectively. What values can $F$ take?