Question

Find the largest number that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively :

• A. 77
• B. 85
• C. 17
• D. 15

Answer 1

Answer:

C. 17

Let the required largest number be (d).

Since the remainders are 7, 11, and 15:

398-7=391
436-11=425
542-15=527
So (d) must exactly divide 391, 425, and 527.

Now find their HCF (GCD):

$391 = 17 \times 23$
$425 = 17 \times 25$
$527 = 17 \times 31$

Common factor (=17).

Therefore, the largest number is:

$\boxed{17}$