Question

find the largest possible integer that will divide 398,436,
542 and leaving remainder 7,11,25​

Answer 1

Answer:

We need to find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively. Hence, we need to find the HCF of 3 numbers (398-7), (436-11) and (542-15).

Hence,

398 - 7 = 391

436 - 11 = 425

542 - 15 = 527

Now, you can find the hcf (391, 425, 527) = 17

Hence, the largest number that will divide 398,436 and 542 leaving remainders 7, 11 and 15 respectively is 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.