5814-5430=384; 5958-5430=528; 5958-5814=144 are each multiples of N, because the remainders after dividing by N are the same, and:
384=3×27; 528=24×3×11; 144=24×32 have HCF=3×24=48, which is the largest value for N (answer option 4).
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Of these, 4 are 2-digit numbers (including itself) (answer option 3).