Worksheet: Prime and Composite Numbers

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

Q1:

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

Q2:

Is 21 a prime or a composite number?

  • Aa prime number
  • Ba composite number

Q3:

Is 23 a prime or a composite number?

  • Aa composite number
  • Ba prime number

Q4:

All prime numbers are odd except .

Q5:

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

  • Aprime
  • Bcomposite
  • Cneither prime nor composite

Q6:

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.

Q7:

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.

Q8:

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.

Q9:

What is the greatest prime number between 15 and 24?

Q10:

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

Q11:

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

  • Aprime
  • Bcomposite

Q12:

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

Q13:

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

Q14:

Which of the following is a prime number?

  • A43
  • B45
  • C8
  • D4

Q15:

Is 96 a prime number?

  • Ayes
  • Bno

Q16:

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

  • Ano
  • Byes

Q17:

Which of the following is not a prime number?

  • A23
  • B73
  • C68
  • D2

Q18:

Find a prime number between 37 and 46.

Q19:

Look at these numbers.

How many of these numbers are prime?

Which is the largest prime number?

Which is the smallest composite number?

Q20:

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

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

Q21:

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

Q22:

Find the smallest prime number that is greater than 40.

Q23:

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

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

Q24:

How many prime numbers have integers as their square roots?

Q25:

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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