Question

Find the largest possible positive integer that will divide 398, 436 and
542 leaving remainder 7, 11, 15 respectively

Answer 1

Hey,sup!

As per the question,

398-7=391.
436-11=425.
542-15=527.

Factors of 391=17×23.
425=5×5×17.
527=17×31.

Hcf = 17.

So,17 is the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.

Hope it helps.

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.