Question

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

Answer 1

the numbers are

398-7 =391

436-11 =425

then

HCF of 391, 425 and 527 is

(425, 391)

425 =391 x 1 + 34

391 =34 x 11 + 17

34=17 x 2 + 0

so HCF is 17

now HCF of

(17, 527)

527 =17 x 31 + 0

:. HCF of numbers = 17

so the required number is 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.