Multiple choice

Which of the following options is the greatest number, which when divides 211, 270 and 321 leaves 4, 9 and 6 as remainders respectively?

  1. 2

  2. 3

  3. 6

  4. 9

  5. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need the HCF of (211-4), (270-9), and (321-6), which are 207, 261, and 315. The HCF of 207, 261, and 315 is 9.

AI explanation

Subtract the remainders from the respective numbers to get 207, 261, and 315. The required number must be the highest common factor of these three new numbers. Prime factorization reveals 207 = 9 * 23, 261 = 9 * 29, and 315 = 9 * 35. Since 23, 29, and 35 share no common factors, their highest common factor is 9. The required number is 9.

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