Question

in which largest number if we divide 398 for 36 and 5:42 then the reminder will be 7 11:15

Answer 1

The largest positive integer that will divide 398, 436 and 542 leaving reminders 7, 11 and 15 respectively is the HCF of the numbers (398 – 7), (436 – 11) and (542 – 15) i.e. 391, 425 and 527.

HCF of 391,425 and 527:

HCF of 425 and 391:
425 = 391 x 1 + 34
391 = 34 x 11 + 17
34 = 17 x 2 + 0

HCF of 425 and 391 = 17

Similarly, HCF of 17 and 527 = 17

Thus, HCF of 391, 425 and 527 = 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.