Multiple choice

Find the greatest number such that 233 divided by that number leaves 5 as remainder; 368 divided by that number leaves 7 as remainder; and 275 divided by that number leaves 9 as remainder.

  1. 18

  2. 19

  3. 17

  4. None of these
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B Correct answer
Explanation

We need the GCD of (233-5), (368-7), and (275-9). GCD(228, 361, 266). 228 = 19 * 12, 361 = 19 * 19, 266 = 19 * 14. The GCD is 19.

AI explanation

Using the common remainder theorem, the required number is the HCF of the differences between the numbers and their respective remainders. The differences are 233 minus 5, which is 228; 368 minus 7, which is 361; and 275 minus 9, which is 266. Factoring these differences shows that 19 is their greatest common divisor. The greatest number is 19.

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