Question

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

• A. 527
• B. 13
• C. 17
• D. 491

Answer 1

The correct option is C 17

Since the remainders are 7,11 and 15 respectivey, the required number is the HCF of (398 - 7 = 391), (436 - 11 = 425), and (542 - 15 = 527)

First we find the HCF of 391 and 425 by Euclid's algorithm as given below.

425 = 391 $\times$ 1 + 34

Here remainder is not zero. So applying Euclid's algorithm for 391 and 34.

391 = 34 $\times$ 11 + 17

Here remainder is not zero. So applying Euclid's algorithm for 34 and 17.

34 = 17 $\times$ 2 + 0

Here the remainder is zero.

Clearly, H.C.F of 391 and 425 is 17.

Let us now find the HCF of 17 and the third number 527 by Euclid's algorithm:

527 = 17 $\times$ 31 + 0

Here the remainder is zero.

The HCF of 17 and 527 is 17. Hence, HCF of 391, 4250 and 527 is 17.

Hence, the required number is 17.