Question

find the largest number which divides 398, 436,and 842 leaving remainder 7,11,9 respectively ​

Answer 1

398/17=23 and remainder=7

436/17=25 and remainder=11

842/17=49 and remainder =9

398-7=391, which is divisible by 17 in 23 times.

436-11=425, which is divisible by 17 in 25 times.

842-9=833, which is divisible by 17 in 49 times.

And according to me 17 is the largest number which has divided the three numbers leaving remainders 7,11,9.

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.