Prime and Composite Numbers Quiz

Grade 5 · Math · Quiz

Check your understanding of prime numbers, composite numbers, and prime factorization.

Questions

1. Which list contains ONLY prime numbers?

   1. 2, 4, 7, 11
   2. 3, 5, 7, 11
   3. 3, 9, 11, 13
   4. 2, 5, 9, 13
   Show answer

   Answer: 3, 5, 7, 11

   3, 5, 7, and 11 are all prime. In option A, 4 is composite. In option C, 9 is composite. In option D, 9 is composite.

2. What is the prime factorization of 20?

   1. 4 x 5
   2. 2 x 10
   3. 2 x 2 x 5
   4. 2 x 2 x 2 x 5
   Show answer

   Answer: 2 x 2 x 5

   20 = 2 x 10 = 2 x 2 x 5. Options A and B are valid factor pairs but not full prime factorizations because 4, 5, 10 contain composites. Only 2 x 2 x 5 uses all primes.

3. Which number is composite?

   1. 29
   2. 31
   3. 37
   4. 39
   Show answer

   Answer: 39

   39 = 3 x 13, so it has more than two factors and is composite. 29, 31, and 37 are all prime.

4. How many prime numbers are between 10 and 20?

   1. 2
   2. 3
   3. 4
   4. 5
   Show answer

   Answer: 4

   The prime numbers between 10 and 20 are 11, 13, 17, and 19. That is 4 prime numbers.

5. What is the prime factorization of 45?

   1. 5 x 9
   2. 3 x 15
   3. 3 x 3 x 5
   4. 3 x 3 x 3 x 5
   Show answer

   Answer: 3 x 3 x 5

   45 = 9 x 5 = 3 x 3 x 5. Options A and B use non-prime factors (9 and 15). The correct prime factorization is 3 x 3 x 5.

6. A prime number always has:

   1. More than two factors
   2. Exactly one factor
   3. Exactly two factors
   4. An odd number of factors
   Show answer

   Answer: Exactly two factors

   A prime number is defined as having exactly two factors: 1 and itself. This is what distinguishes primes from composites and from 1.

7. Every composite number can be written as a product of prime numbers.

   Show answer

   Answer: True

   This is called the Fundamental Theorem of Arithmetic: every whole number greater than 1 can be written as a unique product of prime numbers.

8. Write the prime factorization of 28 as a multiplication expression: 2 x 2 x ___.

   Show answer

   Answer: 7

   28 = 4 x 7 = 2 x 2 x 7. The prime factorization of 28 is 2 x 2 x 7.

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