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Quiz about Composite Numbers
Quiz about Composite Numbers

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.
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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
992
Awards
Top 35% Quiz
- -
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)
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


Question 3 of 10
3. The number 1 is not a prime number. So is it a composite number?


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)?


Question 5 of 10
5. All even numbers greater than 2 are composite numbers.


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


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


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


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


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



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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.
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?

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.
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?

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.
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?

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.
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.)

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.
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 ___.

Answer: Arithmetic

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

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

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