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# Perfect Numbers Trivia Quiz

### Let's explore the amazing properties of these interesting and intriguing perfect numbers. Can you score a perfect 10 out of 10 for this quiz? Enjoy!

A multiple-choice quiz by Matthew_07. Estimated time: 4 mins.

Author
Time
4 mins
Type
Multiple Choice
Quiz #
277,465
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
6 / 10
Plays
1472
Awards
Top 35% Quiz
Last 3 plays: Guest 2 (5/10), Guest 152 (4/10), Guest 173 (3/10).
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Question 1 of 10
1. A perfect number is a positive integer which is the sum of its divisor, excluding the number itself. For example, the first perfect number 6 can be expressed as 1 x 6 or 2 x 3. Notice that 6 = 1 + 2 + 3. If we want to include the perfect number itself in the definition, we will say that a perfect number is ______ of the sum of all of its divisors. Hint

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Question 2 of 10
2. The first perfect number is 6. Which of the following is the second perfect number? (The divisors are given in bracket) Hint

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Question 3 of 10
3. Notice the following pattern:
The first perfect number has 1 digit; the second perfect number has 2 digits; the third one has 3 digits; and the fourth one has 4 digits. So, does the fifth perfect number contain 5 digits?

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Question 4 of 10
4. The sum of all of the reciprocals of a perfect number's factors (including the perfect number itself) equals? Hint

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Question 5 of 10
5. The fundamental theorem for finding perfect numbers states that if (2^n)-1 is a (an) _____ number, then 2^(n-1) x [(2^n)-1] is a perfect number. Hint

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Question 6 of 10
6. The first 4 perfect numbers can be generated by using the formula 2^(n-1) x [(2^n)-1], where n = 2, 3, 5, 7. This formula was discovered by? Hint

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Question 7 of 10
7. The formula 2^(n-1) x [(2^n)-1] is used to locate the next perfect number. As of 2006, the 44th perfect number has been found, which contains 19,616,714 digits. The second part of the formula, [(2^n)-1], which is a number that is one less than a power of 2, is called a ______ number. Hint

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Question 8 of 10
8. The last digit of all of the 44 perfect numbers discovered by now (as of November 2007) is either 6 or 8.

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Question 9 of 10
9. Complete the following quote taken from an ancient Christian scholar, Saint Augustine's book, "The City of God". "God created all things in ___ days because the number is perfect."

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Question 10 of 10
10. GIMPS offers free software for volunteers to download and locate the next prime and perfect number. GIMPS stands for? Hint

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Most Recent Scores
Jul 23 2024 : Guest 2: 5/10
Jul 21 2024 : Guest 152: 4/10
Jun 27 2024 : Guest 173: 3/10
Jun 18 2024 : Guest 103: 6/10

Score Distribution

Quiz Answer Key and Fun Facts
1. A perfect number is a positive integer which is the sum of its divisor, excluding the number itself. For example, the first perfect number 6 can be expressed as 1 x 6 or 2 x 3. Notice that 6 = 1 + 2 + 3. If we want to include the perfect number itself in the definition, we will say that a perfect number is ______ of the sum of all of its divisors.

Notice that 6 = 1 x 6 = 2 x 3. The sum of all the divisors is 12. So, 6 is half of all of the divisors.
2. The first perfect number is 6. Which of the following is the second perfect number? (The divisors are given in bracket)

Answer: 28 (1, 2, 4, 7, 14, 28)

Both 26 and 27 are composite numbers, meaning that they can be expressed as multiplication of smaller prime numbers, that is, 26 = 2 x 13 and 27 = 3 x 3 x 3.

On the other hand, 28 is the second perfect number, since 28 = 1 + 2 + 4 + 7 + 14, or 28 = 0.5 x (1 + 2 + 4 + 7 + 14 + 28).

Last but not least, 29 is a prime number, since this number can only be divided without remainder by 1 and the number itself.
3. Notice the following pattern: The first perfect number has 1 digit; the second perfect number has 2 digits; the third one has 3 digits; and the fourth one has 4 digits. So, does the fifth perfect number contain 5 digits?

The fifth perfect number is 33550336, which has 8 digits.
4. The sum of all of the reciprocals of a perfect number's factors (including the perfect number itself) equals?

For example, the factors of the first perfect number 6 are 1, 2, 3, 6. Observe that 1/1 + 1/2 + 1/3 + 1/6 = 2.
5. The fundamental theorem for finding perfect numbers states that if (2^n)-1 is a (an) _____ number, then 2^(n-1) x [(2^n)-1] is a perfect number.

This theorem was provided by Euclid in his book "Elements".
6. The first 4 perfect numbers can be generated by using the formula 2^(n-1) x [(2^n)-1], where n = 2, 3, 5, 7. This formula was discovered by?

The first four perfect numbers are:
(2^1)x[(2^2)-1] = 6 = 1 + 2 + 3
(2^2)x[(2^3)-1] = 28 = 1 + 2 + 4 + 7 + 14
(2^4)x[(2^5)-1] = 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
(2^6)x[(2^7)-1] = 8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064
7. The formula 2^(n-1) x [(2^n)-1] is used to locate the next perfect number. As of 2006, the 44th perfect number has been found, which contains 19,616,714 digits. The second part of the formula, [(2^n)-1], which is a number that is one less than a power of 2, is called a ______ number.

Mersenne numbers are named after a French monk, Marin Mersenne.
8. The last digit of all of the 44 perfect numbers discovered by now (as of November 2007) is either 6 or 8.

It still remains as an open question in the field of mathematics whether there is any odd perfect number.
9. Complete the following quote taken from an ancient Christian scholar, Saint Augustine's book, "The City of God". "God created all things in ___ days because the number is perfect."

Perfect numbers appear in many natural phenomena. Another example would be the moon's period of 28 days, where 28 is the second perfect number!
10. GIMPS offers free software for volunteers to download and locate the next prime and perfect number. GIMPS stands for?

Answer: Great Internet Mersenne Prime Search

Yes, you can also be a part of this project. The last three Mersenne prime numbers were discovered by volunteers.

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I hope you enjoyed this quiz. Any comments are most welcomed. Have a nice day!
Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
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Related Quizzes
This quiz is part of series Fun with Numbers:

A collection of my mathematics quizzes, covering different types of numbers with interesting properties. This list includes composite numbers, consecutive numbers, Fibonacci numbers, palindromic numbers, perfect numbers, prime numbers, square numbers, and triangular numbers.

1. Composite Numbers Average
2. Consecutive Numbers Average
3. Fibonacci Numbers Average
4. Palindromic Numbers Average
5. Perfect Numbers Average
6. Prime Numbers Tough
7. Square Numbers Average
8. Triangular Numbers Average

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