When 5430, 5814 and 5958 are divided by the whole number N, the remainder is the same. What is the largest possible value of N? and how many 2 digit values can n assume?

Question

Answers

For largest value options

1. 144.      2. 96.     3. 72.    4.48.    5.24.  

For 2digit values

1. 1.      2. 2.     3. 4.      4.8.      5.10.

Answer 1

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).