Question

Find the largest positive integers that will divide 398, 436, and 542 leaving remainder 7, 11 and 15.

If you give me the answer as 17, explain how can 17 divide 398 leave a remainder 7 when 17/398 is a fraction?

By the way, explain if there is any difference between
a divide b
a divide by b
a divided by b
Are all of them a/b?

Answer 1

The answer is 17 because it's 398/17 not 17/398.

Thus a divide b means b/a

a divided or divide by b means a / b

Hope it's helpful.

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.