Question

find the largest positive integer that will divide 398 ,436 and 542 leaving remainders 7, 11 and 15 respectively

Answer 1

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Dividing 398 by the required number there is a remainder of 7

It means that :-

398 – 7 = 391

Similarly,

436 -11 = 425

542 – 15 = 527 are exactly divisible by the required number.

HCF of 391, 425 and 527.

Using Euclid’s division algorithm.

425 = 391 x 1 + 34

391 = 34 x 11 + 17

34 = 17 x 2 + 0

HCF = 17

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Answer 2

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the numbers are

398-7 =391

436-11 =425

then

HCF of 391, 425 and 527 is

(425, 391)

425 =391 x 1 + 34

391 =34 x 11 + 17

34=17 x 2 + 0

so HCF is 17

now HCF of

(17, 527)

527 =17 x 31 + 0

:. HCF of numbers = 17

so the required number is 17

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