Question

Find the largest number that divides 398,436 and 542 leaving remainders 7,11 and15

Answer 1

First of all, we need to subtract the remainders
Prime factorisation:-
391 = 17 X 23
425 = 5 X 5 X 17
527 = 17 X 31
HCF = 17 Hope it’ll help

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.