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Question
What is the largest positive integer that divides 401 , 436 and 542 leaving remainder 10,11 and 15 respectively?
What is the largest positive integer that divides 401 , 436 and 542 leaving remainder 10,11 and 15 respectively?
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Solution
The correct option is C 17
If the integer leaves remainder 10 , on dividing 401, then it divides 391 exactly
If the integer leaves remainder 11 , on dividing 436, then it divides 425 exactly
If the integer leaves remainder 15 , on dividing 542, then it divides 527 exactly
On prime factorizing , 391 , 425 and 527 , we have
391 = 17 x 23
425 = 5x 5 x 17
527 = 17 x 31
The HCF of , 391 , 425 and 527 =17
Therefore the largest positive integer that divides 401 , 436 and 542 leaving remainder 10,11 and 15 respectively is 17.
17
If the integer leaves remainder 10 , on dividing 401, then it divides 391 exactly
If the integer leaves remainder 11 , on dividing 436, then it divides 425 exactly
If the integer leaves remainder 15 , on dividing 542, then it divides 527 exactly
On prime factorizing , 391 , 425 and 527 , we have
391 = 17 x 23
425 = 5x 5 x 17
527 = 17 x 31
The HCF of , 391 , 425 and 527 =17
Therefore the largest positive integer that divides 401 , 436 and 542 leaving remainder 10,11 and 15 respectively is 17.
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