Question

Find the largest positive interger that will divide 398,436and542 leaving remainder 7,11 and 15 respectively

Answer 1

398-7=391
436-11=425
542-15=527
HCF of 391,425,527:
391=17*23
425=17*5*5
527=17*31
HCF=17
Therefore, the largest positive integer is 17
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.