Given number 34k56k is divisible by 6 . So it must be divisible by 2 and 3 (both are factor of 6). Divisibility rule of 2→ The last digit must be even or 0 . So, it may be 0,2,4,6 and 8 Divisibility rule of 3→ The sum of all digits must be divisible by 3 . ∴ Sum of digits =3+4+k+5+6+k =18+2k For k=3,6 and 9 , given number is divisible by 3 . But here only 6 is even value of k. ∴k=6 ∴ Largest value of k=6.