Question

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?

Answer 1

We can write:

5430=aN+r,

5814=bN+r,

5958=cN+r,

where a, b, c are multipliers and r is the common remainder.

5814-5430=384=N(b-a),

5958-5814=144=N(c-b).

384/144=8/3=(b-a)/(c-b)

So, if b-a=8 and c-b=3 then N=384/8=144/3=48.

N=48 is the largest value for N.

[5430=48a+r; a=113, r=6,

5814=48b+6, b=121,

5958=48c+6, c=124.]