Question

find the largest positive integer that will divide 398,436,542 living remember 7,11,15 respectively

Answer 1

numbers

398 - 7 = 391

436 - 11 = 425

542 - 15 = 527

Now HCF of these numbers

[Use Euclids division  algoritham method if you studied

425  = 391 * 1 + 34 (reminder is not equal to 0)

391 = 34 * 11 + 17 ( reminder is not equal to 0)

34 = 17 * 2 + 0 (reminder is 0)

So HCF of 391 and 425 is 17

So try on 542 with 17. yes it can be divided with 17.]

If not 391 = 17 x 23

425 = 27 x 25

542 = 17 x 31

HCF of 391, 425 and 527 is 17

So 17 is the largest number

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.