Question

Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively. [4 MARKS]

Answer 1

Concept : 1 Mark
Calculation : 2 Marks
Conclusion : 1 Mark

Clearly, the required number is the HCF of the numbers

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.