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

Posted by Nisha Yadav 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

The largest positive integer that will divide 398, 436 and 542 leaving reminders 7, 11 and 15 respectively is the HCF of the numbers (398 – 7), (436 – 11) and (542 – 15) i.e. 391, 425 and 527.
HCF of 391,425 and 527:
HCF of 425 and 391:
425 = 391 × 1 + 34
391 = 34 × 11 + 17
34 = 17 ×2 + 0
HCF of 425 and 391 = 17
527 = 17 × 31
Similarly, HCF of 17 and 527 = 17
So, HCF of (391,425 ,527) = 17
∴ Required number is 17.

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