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Real numbers

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

Puspita Chattopadhyay

Hi Puspita Chattopadhyay !
Mark as answer and close

It is given that 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.

In other words, required number is a factor of 391.

Similarly, required positive integer is a factor of 436 – 11 = 425 and 542 – 15 = 527.

Clearly, required number is the HCF of 391, 425 and 527.

Using the factor tree, we get the prime factorization of 391, 425 and 527.

Using factor tree, we get prime factorization . .

391 = 17 x 23

425 = 17 x 25 [17 x 52]

527 = 17 x 31

Therefore, HCF of 391, 425 and 527 is 17.

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