Multiple choice

12 Find the greatest number which divides the number 4061, 4185 and 4227 leaving remainders 2, 3 and 4, respectively.

  1. 43

  2. 41

  3. 48

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Find the HCF of (4061-2), (4185-3), and (4227-4), which is the HCF of 4059, 4182, and 4223. 4059 = 41 * 99, 4182 = 41 * 102, 4223 = 41 * 103. The HCF is 41.

AI explanation

Subtract the respective remainders from the numbers to get 4059, 4182 and 4223. The required number is the HCF of these new values. Since 4059 = 99 times 41, the number 41 divides 4059 exactly. It also divides 4182 as 4182 = 102 times 41, and it divides 4223 as 4223 = 103 times 41. Therefore, the greatest number is 41.

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