When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

• let the divisor be x.
  242-8 i.e. 234is divisible by x
  similarly 698-9 i.e. 689 and 940-4 i.e. 936 are divisible by x.
  x = HCF(234, 689, 936)= 13.
• 8 years agoHelpfull: Yes(1) No(0)
• 242=8(mod x)
  698=9(mod x)
  => (242+698) = (8+9)(mod x) (addition theorem.)
  (242+698) = 4(mod x) (Given)
  so value 8+9 must be equivalent to x that means x is 13(8+9-4) and which is correct.
• 9 years agoHelpfull: Yes(0) No(0)