Question

Find the largest number that will be divided 398,436 and 540 leaving the reminder 7,11,15 respectively.

Answer 1

On dividing 398 by the required number, there is a remainder of 7. This means that 398 7 = 391 is exactly divisible by the required number. Similarly, 436 -11 = 425 and 542 15 = 527 are exactly divisible by the required number.

The HCF of two positive integers is the largest positive integer that divides both the integers.

So, the required number will be the HCF of 391, 425 and 527. And that can be found by using Euclids division algorithm.

425 = 391 x 1 + 34

391 = 34 x 11 + 17

34 = 17 x 2 + 0

Thus, HCF = 17

Hence, the required number is 17.