Question

What is The largest that will divide the 398, 606 and 474 leaving remainders 7, any 1 and 15 respectively is

Answer 1

Hi friend,

398 - 7 = 391

606 - 1 = 605

474 - 15 = 459

THEREFORE,

Required number = HCF(391,605,459)

Now,

391 = 17×23

605 = 11×11 × 5

459 = 3×3×3×17

THEREFORE,

HCF OF 391,605,459 = 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.