Question

Find the largest number which divides 398 436 and 452 leaving remainder 7 11 and 10 respectively

Answer 1

the no. which divides 398,436&452 leaves remainder 7,11&10 is hcf of 398-7,436-11&452-10
then hcf of 391,425&442 is 17
hence our answer is 17

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.