Question

Find the largest possible integer that will divide 398, 436 and 542 leaving remainders 7,11 and 15 respectively

Answer 1

First deduct the remainders from each term

398 - 7 =391

436–11 = 425

542–15 =527

Next find the HCF of the terms that you get

391 = 17x23

425 = 5x5x17

527 = 17x31

The HCF is 17.

The answer is the HCF or 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.