Question

The largest number that will divide 398,436 and 542 leaving remainders 7, 11 and 15 respectively is *

Answer 1

Step-by-step explanation:

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

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Answer 2

Sure, here is your answer:

Step 1- Subtract the remainders from the numbers. 398-7=391, 436-11=425,

542-15=527.

Step 2- Find the highest common factor of these numbers... [Hope you know how to find the HCF :)] when we do so, we get: 17

There is your answer! Isn't it easy?!

Hope it helps!