Explanation:

Remainder in case of 148 = 4

Number = 148 - 4 = 144

Remainder in case of 246 = 6

Number = 246 - 6 = 240

Remainder in case of 623 = 11

Number = 623 - 11 = 612

Now, we have find the H.C.F. of 144. 240 and 612
        _____________
    2  | 144, 240, 612
        |____________
    2  |   72, 120, 306   
        |____________
    3  |   36,  60,  153  
        |____________
        |   12,  20,  51

H.C.F. of 144, 240 and 612 = 2*2*3 = 12

Therefore, the required number is 12 that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively.

Hence, optin 4 is the correct answer.