Multiple choice

$Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively.$ That number can be possible:- A. 19 B. 17 C. 13 D. 9

  1. All A, B, C and D

  2. Only B and C

  3. Only D and B

  4. Only A

  5. Only B
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

If a number N divides 400, 435, 541 leaving remainders 9, 10, 14 respectively, then N divides (400-9), (435-10), (541-14) = 391, 425, 527 exactly. Find HCF of 391, 425, 527. 391 = 17 × 23, 425 = 17 × 25, 527 = 17 × 31. HCF = 17. Check: 400 ÷ 17 = 23 remainder 9 ✓, 435 ÷ 17 = 25 remainder 10 ✓, 541 ÷ 17 = 31 remainder 14 ✓. So 17 is the greatest such number. 19 and 13 don't work, and 9 is less than 17.

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