Question

find the greatest number that divide 398 436 and 542 leaving a remainder of 7 11 and 15 respectively

Answer 1

17 would be the answer ,398-7=391,436-11=425 ,542-15=527.
17 is the greatest number which is dividing all (391,425,527) exactly. so when we will divide these numbers (398,436,542) ,it will leave the remainders 7, 11,and 15.hence 17 is the correct answer !

Answer 2

Given :-

398 , 436 and 542

To Find :-

The largest number

Solution :-

Let’s assume the integer is x

According to the condition given in the question

⇒ xy+7 = 398

⇒  xz+11 = 436

⇒  xk+15 = 542

⇒ xy =391

⇒  xz = 425

⇒  xk = 527

⇒  17 × 23 = 391

⇒  17 × 25 = 425

⇒ 17 × 31 = 527

So, the largest possible integer that will divide 398,436,542 & leaves reminder 7,11 and 15 respectively was 17.