What is the greatest number that divides 398, 436 and 542, leaving remainders 7, 11 and 15 respectively?

17Correct answerYour answer23Correct answerYour answer25Correct answerYour answer31Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Subtract each remainder: $398 - 7 = 391$ , $436 - 11 = 425$ , $542 - 15 = 527$ .
The required number is HCF(391, 425, 527).
$391 = 17 \times 23$ , $425 = 17 \times 25$ , $527 = 17 \times 31$ , so the HCF is 17.

Worth noting

23 divides only 391, 25 only 425 and 31 only 527. The answer must divide all three after the remainders are removed.

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Explanation