Worksheet: Prime and Composite Numbers

In this worksheet, we will practice deciding whether a number is prime or composite.


What is a composite number?

  • Aa number with more than two factors
  • Ba number that has one factor repeated
  • Ca number with exactly two factors, 1 and itself
  • Da number with exactly two factors, 0 and itself
  • Ea number with exactly two factors, 0 and 1


Is 21 a prime or a composite number?

  • Aa prime number
  • Ba composite number


Is 23 a prime or a composite number?

  • Aa composite number
  • Ba prime number


All prime numbers are odd except .


Determine whether the number 85 is prime, composite, or neither.

  • Aprime
  • Bcomposite
  • Cneither prime nor composite


Michael is learning about prime numbers. He knows that 5 is a prime number, because the only factors of 5 are 1 and 5.

Is 9 a prime number? Why?

  • AYes, because its only factors are 1 and 9.
  • BNo, because 3 is a factor.


Benjamin says that 1 is a prime number because it only has 1 factor pair.

Is he correct? Why?

  • AYes, 1 only has one factor.
  • BNo, because all odd numbers are prime.
  • CNo, prime numbers have more than two factors, 1 only has one factor.
  • DNo, prime numbers have two factors, 1 only has one factor.
  • EYes, because all odd numbers are prime.


Madison says that every even number is composite because 2 is a factor.

Is she correct? Why?

  • AYes, because all odd numbers are prime.
  • BYes, because 2 is even and composite.
  • CYes, because 2 is an even number.
  • DNo, because 2 is even and composite.
  • ENo, because 2 is even and prime.


What is the greatest prime number between 15 and 24?


The table shows all the factors of some numbers.

Number (𝑥)101133157145
Factor of (𝑥)1, 1011, 7, 19, 1331, 1571, 5, 29, 145

Which of the numbers are prime?

  • A101 and 157
  • B157 and 145
  • C133 and 145
  • D133 and 157
  • E101 and 133


Caribou calves weigh about 13 pounds at birth. Is the number 13 a prime or a composite number?

  • Aprime
  • Bcomposite


A teacher asked her class to color all the prime numbers between 1 and 10. Here are some of their answers. Which one is correct?

  • A
  • B
  • C
  • D
  • E


Isabella bought these four raffle tickets, and one of them was the winning ticket.

The winning number is a prime number between 10 and 20. Which of her tickets won the prize?

  • Aticket number 34
  • Bticket number 23
  • Cticket number 18
  • Dticket number 15
  • Eticket number 17


Which of the following is a prime number?

  • A43
  • B45
  • C8
  • D4


Is 96 a prime number?

  • Ayes
  • Bno


Are the numbers 2, 47, and 79 prime numbers?

  • Ano
  • Byes


Which of the following is not a prime number?

  • A23
  • B73
  • C68
  • D2


Find a prime number between 37 and 46.


Look at these numbers.

How many of these numbers are prime?

Which is the largest prime number?

Which is the smallest composite number?


State two prime numbers that are greater than 15 and less than 95.

  • A44, 60
  • B45, 61
  • C43, 59
  • D42, 58


All odd numbers greater than 7 can be expressed as the sum of three prime numbers. Which three prime numbers have a sum of 97?

  • A17, 19, 61
  • B17, 18, 62
  • C16, 20, 61
  • D18, 19, 60


Find the smallest prime number that is greater than 40.


Which of the following integer sequences is not guaranteed to have infinitely many primes?

  • A2𝑛+5
  • B2𝑛+4
  • C2𝑛+3
  • D2𝑛+1


How many prime numbers have integers as their square roots?


How many prime numbers are there, and why?

  • AWe do not know, because computers are not powerful enough to compute as largely as we need.
  • BInfinitely many in theory, as you could theoretically extend the sieve of Eratosthenes indefinitely.
  • CInfinitely many, otherwise you could simply take the product of all of them and add one.
  • DFinitely many, because once you reach a certain size, every number factors into smaller primes.

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