VTMO 2026 - Grade 7 - Final - SET 8 - Self-study Question 3

Let $M=\overline{abcdefgh}$ be an eight-digit number using each of $1,2,3,4,5,6,7,8$ once. Its two-digit prefix is divisible by 2, its three-digit prefix by 3, and so on up to its eight-digit prefix being divisible by 8. Find $M$.