Question

11) Find out the largest divisor for the numbers 389, 436 and 542 that would give 4, 7 and 3 respectively as remainders.
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Answer 1

Answer:

We will find the HCF of 391, 425 and 527 by prime factorization method.

391=17×23

425=52×17

527=17×31

Hence, HCF of 391, 4250 and 527 is 17 because the greatest common factor from all the numbers is 17 only.

Step-by-step explanation:

Complete step-by-step answer:

Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.

And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.

Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527

We will find the HCF of 391, 425 and 527 by prime factorization method.

391=17×23

425=52×17

527=17×31

Hence, HCF of 391, 425 and 527 is 17 because the greatest common factor from all the numbers is 17 only.

So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.