Multiple choice

Out of the four numbers 420, 385, 231 and 363, you can delete any one number and the HCF of remaining three numbers is found. What is the maximum possible HCF you can get?

  1. 3

  2. 5

  3. 7

  4. 11

  5. 33
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D Correct answer
Explanation

Numbers: 420 (2^2*3*5*7), 385 (5*7*11), 231 (3*7*11), 363 (3*11^2). If we remove 420, HCF(385, 231, 363) = HCF(5*7*11, 3*7*11, 3*11^2) = 11.

AI explanation

To maximize the highest common factor of three remaining numbers, you must delete the number that lacks the largest common prime factor. Factoring the numbers reveals that 420 is divisible by 11, 231 is divisible by 11, and 363 is divisible by 11, while 385 is divisible by 11 and 5, but wait, 385 is also divisible by 11; checking the provided factoring, 385, 231 and 363 share no large factor, but 420, 231 and 363 share 11 as 420 is 11 times 38 plus 2, wait, 420 is not divisible by 11. Factoring accurately, 385 equals 5 times 7 times 11, 231 equals 3 times 7 times 11, and 363 equals 3 times 11 squared, meaning if you delete 420, the remaining three numbers share an HCF of 11.

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