Question

Find the greatest pisitive integer which will divide 398 , 436 and 542 leaving remainder 7, 11 and 15 respectively.

Answer 1

Hello there !!

When the given numbers are divided by a certain number , they leave some remainders .
To find the greatest positive integer , that will divide the numbers , leaving  some remainders , follow the given steps :-

1) Subtract the remainders from the respective dividends.
398 - 7 = 391
436 - 11 =  425
542-15 = 527

2) Find the HCF of the numbers obtained !!
391 = 17 x 23
425 = 5 x 5 x 17 
527 = 17 x 31

3) HCF = 17

Hence , the  greatest positive integer which will divide 398 , 436 and 542 leaving remainder 7, 11 and 15 respectively is 17.

Hope this Helps You !!

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.