Multiple choice

Which of the following is the remainder when a prime number greater than 1000 is divided by 6?

  1. 1

  2. 1 or 3

  3. 1 or 5

  4. 5

  5. 2 or 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

All prime numbers greater than 3 are of the form 6n + 1 or 6n + 5. Since any prime greater than 1000 must be greater than 3, the remainder when divided by 6 must be 1 or 5.

AI explanation

Any integer can be expressed in the form 6k, 6k plus 1, 6k plus 2, 6k plus 3, 6k plus 4 or 6k plus 5. A prime number greater than 6 cannot be of the form 6k, 6k plus 2, 6k plus 3 or 6k plus 4 because those forms are divisible by 2 or 3, making them composite numbers. Thus, any prime number greater than 6 must be of the form 6k plus 1 or 6k plus 5. Dividing these forms by 6 leaves a remainder of 1 or 5, so the remainder when a prime number greater than 1000 is divided by 6 is 1 or 5.

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