Virtual Labs

1. Which of the following is a perfect number?

a: 6 Explanation

Explanation

b: 8 Explanation

Explanation

c: 10 Explanation

Explanation

d: 12 Explanation

Explanation

2. What is a proper divisor of a number?

a: A divisor less than the number itself Explanation

Explanation

b: A divisor equal to the number Explanation

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c: A divisor greater than the number Explanation

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d: Any number Explanation

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3. Which of the following is the continued fraction representation of 7/3?

a: 2 1 3 Explanation

Explanation

b: 2 3 1 Explanation

Explanation

c: 3 2 1 Explanation

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d: 1 2 3 Explanation

Explanation

4. Which of the following numbers is NOT a perfect number?

a: 28 Explanation

Explanation

b: 496 Explanation

Explanation

c: 12 Explanation

Explanation

d: 8128 Explanation

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5. What is the sum of the proper divisors of 28?

a: 14 Explanation

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b: 28 Explanation

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c: 56 Explanation

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d: 27 Explanation

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6. Which of the following best describes a continued fraction?

a: A sum of fractions with increasing denominators Explanation

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b: A representation of a number as an integer part and a sequence of reciprocals Explanation

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c: A product of fractions Explanation

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d: A decimal expansion Explanation

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7. Which of the following numbers is the next perfect number after 28?

a: 120 Explanation

Explanation

b: 496 Explanation

Explanation

c: 8128 Explanation

Explanation

d: 2016 Explanation

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8. Which of the following statements about perfect numbers is true?

a: All perfect numbers are even Explanation

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b: All perfect numbers are odd Explanation

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c: No perfect numbers exist Explanation

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d: All perfect numbers are prime Explanation

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9. What is the continued fraction sequence for 239/51?

a: 4 1 2 5 2 Explanation

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b: 2 1 2 2 Explanation

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c: 1 2 3 4 5 Explanation

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d: 5 2 1 4 2 Explanation

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10. Which of the following is NOT a property of perfect numbers?

a: They are equal to the sum of their proper divisors Explanation

Explanation

b: They are always even (as far as known) Explanation

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c: They are always prime Explanation

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d: They are rare Explanation

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Beauty of Numbers