Question

the largest number that divides 398,436 and 542 leaving remainders 7 , 11 and 15 respectively

Answer 1

* (398 -7) = 391

* ( 436 -11 ) = 425

* ( 542-15 ) = 527

Now,

We have to find HCF of above number

[solution is in attachment]

HCF = 17

So, 17 is the required no.


@Altaf

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.