Virtual Labs

1. Which of the following is the smallest perfect number?

a: 6 Explanation

Explanation

b: 12 Explanation

Explanation

c: 28 Explanation

Explanation

d: 496 Explanation

Explanation

2. What is the sum of the proper divisors of 12?

a: 12 Explanation

Explanation

b: 16 Explanation

Explanation

c: 28 Explanation

Explanation

d: 1 + 2 + 3 + 4 + 6 Explanation

Explanation

3. Which of the following is the continued fraction sequence for 27/10?

a: 2 1 2 2 Explanation

Explanation

b: 4 1 2 5 2 Explanation

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c: 2 2 1 2 Explanation

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d: 1 2 2 2 Explanation

Explanation

4. Which of the following numbers is a perfect number?

a: 15 Explanation

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b: 28 Explanation

Explanation

c: 20 Explanation

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d: 18 Explanation

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5. Which of the following best describes a perfect number?

a: A number that is equal to the sum of its proper divisors Explanation

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b: A number that is prime Explanation

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c: A number that is odd Explanation

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d: A number that is a square Explanation

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6. Which of the following is true about continued fractions?

a: They can represent any rational number Explanation

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b: They can only represent integers Explanation

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c: They are always finite Explanation

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d: They are always infinite Explanation

Explanation

7. What is the next perfect number after 6?

a: 12 Explanation

Explanation

b: 28 Explanation

Explanation

c: 496 Explanation

Explanation

d: 8128 Explanation

Explanation

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

a: All known perfect numbers are even Explanation

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b: No odd perfect numbers are known Explanation

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c: Perfect numbers are always prime Explanation

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d: Perfect numbers are rare Explanation

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

a: 4 1 2 5 2 Explanation

Explanation

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

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

Explanation

c: They are always prime Explanation

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d: They are rare Explanation

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Beauty of Numbers