#05AB1E, 17 bytes

Lε35SÖ4*OygM}.¥sk

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Explanation:

L          # Create a list in the range [1, (implicit) input]
           #  i.e. 15 → [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
 ε         # Map each value to:
  35S      #  Push 35 as digit list: [3,5]
     Ö     #  Check if the current value is divisible by these (1 if truthy; 0 if falsey)
      4*   #  Multiply both by 4
        O  #  And take the sum of that
           #   i.e. 2 → [0,0] → [0,0] → 0
           #   i.e. 9 → [1,0] → [4,0] → 4
           #   i.e. 10 → [0,1] → [0,4] → 4
           #   i.e. 15 → [1,1] → [4,4] → 8
  yg       #  Push the current value again, and pop and push it's length
           #   i.e. 2 → 1
           #   i.e. 15 → 2
  M        #  And then push the largest value on the stack
           #   i.e. 0 and 1 → 1
           #   i.e. 8 and 2 → 8
 }.¥       # After the map: undelta the list (starting from 0)
           #  i.e. [1,1,4,1,4,4,1,1,4,4,2,4,2,2,8]
           #   → [0,1,2,6,7,11,15,16,17,21,25,27,31,33,35,43] 
    sk     # Swap to get the (implicit) input, and get its 0-based index in the list
           #  i.e. 15 → 6
           # (after which the result is output implicitly)