Two numbers when divided by a certain divisor given remainder 437 & 298 respectively. When their sum is divided by the same divisor, the remainder is 236. Find the divisor?

• 499
  
  Let divisor be a and two numbers be x and y.
  Let b and c be the quotient, when x and y is divided by a respectively, then
  ab + 437 = x and ac + 298 = y
  So x+y = a(b+c) + 735
  Given that when (x+y) is divided by a, the remainder is 236, so from above equation a(b+c) is completely divisible by a and the part of the remainder 735 i.e. 735 - 236 = 499 will be divisible by a.
  Hence the required divisor is 499.
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