Question

Find the largest positive integer that will divide 398 439 and 542 leaving remeinder 7, 11 and 15

Answer 1

398 - 7 = 391
439 - 11 = 428
542 - 15 = 527

The HCF of 391, 428 and 527 is 1

The largest number which divides 398, 439 and 542  leaving 7, 11 and 15 respectively as remainders is 1

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.