Question

find the largest number that will divide 398, 436, 542 leaving remainders 7, 11, 15 respectively

Answer 1

We need to find the HCF of three numbers (398-7),(436-11) and (542-15)
Hence,
398-7=391
436-11=425
542-15=527
HCF of( 391, 425 and 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.