Question

find the largest number that divides by 398 436 and542 leaving remainder as 7, 11 and 15 respectively

Answer 1

398-7
436-11
542-15

391=23×1
425=5×5×17

HCF = 17
than 17 is the largest digit that divide this numbers and leaves remainder 7,11,15

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.