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Composite Numbers Trivia Quiz

Let's learn some amazing properties of these intriguing composite numbers. Enjoy!

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

Author
Matthew_07

Time
4 mins

Type
Multiple Choice

Quiz #
287,779

Updated
Dec 03 21

# Qns
10

Difficulty
Average

Avg Score
7 / 10

Plays
1041

Awards
Top 35% Quiz

One at a Time - Single Page - Timed Game

Question 1 of 10

1. A composite number is a positive integer greater than 1 which is not a prime number. Which integer is the smallest composite number?

Answer: (1 digit number)

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Question 2 of 10

2. In biology, cells are the building blocks for organisms. Meanwhile, in chemistry, amino acids are the building blocks for protein. Now, in mathematics, what types of numbers are the building blocks for composite numbers? Hint

Odd numbers

Real numbers

Even numbers

Prime numbers

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Question 3 of 10

3. The number 1 is not a prime number. So is it a composite number?

Yes

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Question 4 of 10

4. Let set A denote the set of prime numbers and set B denote the set of composite numbers. Are these 2 sets disjoint (non-intersecting)?

Yes

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Question 5 of 10

5. All even numbers greater than 2 are composite numbers.

Yes

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Question 6 of 10

6. Composite numbers can be further subcategorized. For example, a semiprime is a type of composite number which is the product of 2 similar or distinct primes. Which of the following numbers is NOT a semiprime? Hint

4 = 2 x 2

9 = 3 x 3

6 = 2 x 3

5 = 1 x 5

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Question 7 of 10

7. Sphenic numbers are another type of composite number. By definition, a sphenic number is a positive integer which is the product of 3 distinct prime numbers. Which of the following is a sphenic number? Hint

30 = 2 x 3 x 5

26 = 1 x 2 x 13

28 = 2 x 2 x 7

34 = 1 x 2 x 17

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Question 8 of 10

8. How many divisors does a sphenic number have? (Hint: A sphenic number is a positive integer which is the product of 3 distinct prime numbers. You can do some combinations and permutations here.) Hint

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Question 9 of 10

9. A theorem states that every natural number which is greater than 1 can be expressed in a unique product of prime numbers. These natural numbers are composite numbers as well. What is the theorem? The Fundamental Theorem of ___. Hint

Calculus

Arithmetic

Algebra

Genera

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Question 10 of 10

10. Another classification of composite numbers is powerful numbers. A powerful number is a positive integer which all the prime factors are repeated. For example, 4 = 2 x 2 and 8 = 2 x 2 x 2 are both powerful numbers. Which of the following is NOT a powerful number? Hint

27 = 3 x 3 x 3

120 = 4 x 5 x 6

343 = 7 x 7 x 7

125 = 5 x 5 x 5

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Quiz Answer Key and Fun Facts

1. A composite number is a positive integer greater than 1 which is not a prime number. Which integer is the smallest composite number?

Answer: 4

0 is a non-positive integer. Meanwhile, 1 is neither prime nor composite. Notice that 4 = 2 x 2. Both 2 and 3 are prime numbers.

Answer: Prime numbers

Every composite number can be factorized or broken down into a product of two or more prime numbers. For example, 12 = 2 x 2 x 3.

3. The number 1 is not a prime number. So is it a composite number?

Answer: No

The number 1 has a very unique property; it is neither prime nor composite.

4. Let set A denote the set of prime numbers and set B denote the set of composite numbers. Are these 2 sets disjoint (non-intersecting)?

Answer: Yes

Yes, any integer greater than 1 is either a prime number or a composite number. However, there exists a number which is neither prime nor composite, namely 1.

5. All even numbers greater than 2 are composite numbers.

Answer: Yes

Observe that all even numbers that are greater than 2 have 2 as one of their prime factors. So they are composite numbers.

Answer: 5 = 1 x 5

5 is a prime number. The first few semiprimes are 4, 6, 9, 10, 14, and 15. From its definition, we can say that the largest semiprime is the square of the largest prime number.

Answer: 30 = 2 x 3 x 5

In fact, 30 is the smallest sphenic number. The first few sphenic numbers are 30, 42, 66, 70, and 78.

Answer: 8

Let say a number x has 3 distinct prime factors, a, b and c. So its divisors are 1, a, b, c, ab, ac, bc and x itself. For example, the divisors for 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The combination and permutation I mean here is 3C1 + 3C2 + 3C3 = 3 + 3 + 1 = 7. And let's not forget that 1 is a factor for any number. So 7 + 1 = 8.

Answer: Arithmetic

The Fundamental Theorem of Arithmetic is also known as the Unique Prime Factorization Theorem.

Answer: 120 = 4 x 5 x 6

Notice that 120 = 4 x 5 x 6 = 2 x 2 x 2 x 3 x 5. So 120 is not a powerful number.

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I hope you learn something new. Comments and feedback are most welcomed. Thanks for playing and have a nice day!

Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

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

Referenced Topics

Science Chemistry Math Biology Definitions Specific Math Topics Theorems

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