Question

Q. Find the largest number which divides 398, 436 and 542 leaving remainder 7, 11 and 15 respectively.

Answer 1

Answer:

Step-by-step explanation:

398 - 7 = 391

436 - 11 = 425

542 - 15 = 527

Hcf of 391 nd 425

425 = 391 × 1 + 34

391 = 34 ×11 + 17

34 ! = 17×2 + 0

Hcf = 17

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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.