Apply the Sieve of Eratosthenes to Identify Prime Numbers

1) Which numbers remain prime between 1 and 20 after applying the sieve?

4, 6, 8

2, 3, 5, 7, 11, 13, 17, 19

9, 15, 21

10, 12, 14

The primes between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

Explanation

The primes between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

2) Which prime factorization is correct for 15?

3 × 5

2 × 15

1 × 15

5 × 6

The prime factorization of 15 is 3 × 5.

Explanation

The prime factorization of 15 is 3 × 5.

3) Which prime numbers remain between 30–40 using the sieve?

31, 32, 33

34, 35, 36

31, 37

38, 39, 40

The primes between 30 and 40 are 31 and 37.

Explanation

The primes between 30 and 40 are 31 and 37.

4) Which of these numbers is prime?

21

25

19

27

The number 19 is prime because it has only two factors.

Explanation

The number 19 is prime because it has only two factors.

5) When crossing out multiples of 3, which of these numbers is eliminated?

13

15

17

19

The number 15 is eliminated because it is a multiple of 3.

Explanation

The number 15 is eliminated because it is a multiple of 3.

6) If you extend the sieve to 50, which is the largest prime below 50?

47

48

49

50

The largest prime below 50 is 47.

Explanation

The largest prime below 50 is 47.

7) Which prime is the largest below 20?

19

17

15

13

The largest prime below 20 is 19.

Explanation

The largest prime below 20 is 19.

8) What happens when multiples of 7 are crossed out up to 50?

Numbers like 14, 21, 28, 35, 42, 49 disappear

Only 7 disappears

All primes disappear

No change

Numbers like 14, 21, 28, 35, 42, 49 disappear

Crossing out multiples of 7 removes 14, 21, 28, 35, 42, and 49.

Explanation

Numbers like 14, 21, 28, 35, 42, 49 disappear

Crossing out multiples of 7 removes 14, 21, 28, 35, 42, and 49.

9) Which number is prime between 40 and 50?

42

44

43

45

The number 43 is prime between 40 and 50.

Explanation

The number 43 is prime between 40 and 50.

10) If we cross out multiples of 2, 3, and 5, which number between 1–30 is still left prime?

21

25

27

29

The number 29 remains prime after crossing out multiples of 2, 3, and 5.

Explanation

The number 29 remains prime after crossing out multiples of 2, 3, and 5.

11) Which number gets crossed out when removing multiples of 3?

9

7

11

13

The number 9 is crossed out when removing multiples of 3.

Explanation

The number 9 is crossed out when removing multiples of 3.

12) Which prime comes directly after 11?

12

17

13

15

The prime number directly after 11 is 13.

Explanation

The prime number directly after 11 is 13.

13) Which of these numbers is composite?

23

29

31

33

The number 33 is composite because 33 = 3 × 11.

Explanation

The number 33 is composite because 33 = 3 × 11.

14) Which pattern of numbers stays when all multiples are crossed out?

Even numbers

Multiples of 5

Prime numbers

Square numbers

When all multiples are crossed out, the numbers left are prime.

Explanation

When all multiples are crossed out, the numbers left are prime.

15) Which number is crossed out first when removing multiples of 11 up to 50?

22

33

44

55

The first number crossed out when removing multiples of 11 is 22.

Explanation

The first number crossed out when removing multiples of 11 is 22.

16) Which prime number comes directly after 37?

38

39

40

41

The prime number after 37 is 41.

Explanation

The prime number after 37 is 41.

17) If the sieve is used up to 30, how many primes remain?

8

9

10

12

There are 10 primes left when using the sieve up to 30.

Explanation

There are 10 primes left when using the sieve up to 30.

18) Which of these is not prime?

41

49

43

47

The number 49 is not prime because 49 = 7 × 7.

Explanation

The number 49 is not prime because 49 = 7 × 7.

19) Which prime number follows 23?

29

27

31

33

The prime number that follows 23 is 31.

Explanation

The prime number that follows 23 is 31.

20) When crossing out multiples of 2, which number disappears first?

1

2

4

5

The first number to disappear when crossing out multiples of 2 is 4.

Explanation

The first number to disappear when crossing out multiples of 2 is 4.

Applying the Sieve to Numbers

1) Which numbers remain prime between 1 and 20 after applying the sieve?

2) Which prime factorization is correct for 15?

3) Which prime numbers remain between 30–40 using the sieve?

4) Which of these numbers is prime?

5) When crossing out multiples of 3, which of these numbers is eliminated?

6) If you extend the sieve to 50, which is the largest prime below 50?

7) Which prime is the largest below 20?

8) What happens when multiples of 7 are crossed out up to 50?

9) Which number is prime between 40 and 50?

10) If we cross out multiples of 2, 3, and 5, which number between 1–30 is still left prime?

11) Which number gets crossed out when removing multiples of 3?

12) Which prime comes directly after 11?

13) Which of these numbers is composite?

14) Which pattern of numbers stays when all multiples are crossed out?

15) Which number is crossed out first when removing multiples of 11 up to 50?

16) Which prime number comes directly after 37?

17) If the sieve is used up to 30, how many primes remain?

18) Which of these is not prime?

19) Which prime number follows 23?

20) When crossing out multiples of 2, which number disappears first?