Understanding The Sieve Method

1) In the sieve, why is 1 not considered a prime?

It has two factors

It only has one factor

It is even

It is composite

The number 1 is not prime because it has only one factor.

Explanation

The number 1 is not prime because it has only one factor.

2) In the sieve, crossing out starts with 2, then 3, then 5, then:

7

13

9

11

After 2, 3, and 5, the next prime is 7.

Explanation

After 2, 3, and 5, the next prime is 7.

3) When using the sieve up to 50, how many primes are found?

12

15

17

20

When using the sieve up to 50, there are 17 primes.

Explanation

When using the sieve up to 50, there are 17 primes.

4) Which pattern do multiples of 3 make on the sieve?

Every second number

Every third number

Every fourth number

Every fifth number

Multiples of 3 form the pattern of every third number.

Explanation

Multiples of 3 form the pattern of every third number.

5) Which prime is the first two-digit number?

9

11

13

17

The first two-digit prime number is 11.

Explanation

The first two-digit prime number is 11.

6) The Sieve of Eratosthenes is used to:

Add numbers

Multiply numbers

Find prime numbers

Find square roots

The Sieve of Eratosthenes is used to find prime numbers.

Explanation

The Sieve of Eratosthenes is used to find prime numbers.

7) After crossing out multiples of 2, which prime is used next?

4

3

5

9

After multiples of 2, the next prime used is 3.

Explanation

After multiples of 2, the next prime used is 3.

8) When using the sieve up to 30, what is the next prime after 2 and 3?

7

9

5

11

The next prime after 2 and 3 is 5.

Explanation

The next prime after 2 and 3 is 5.

9) What pattern do multiples of 2 make on the sieve?

Random numbers

Every second number

Every third number

Every fourth number

Multiples of 2 form the pattern of every second number.

Explanation

Multiples of 2 form the pattern of every second number.

10) The sieve is based on which mathematical property?

Addition

Subtraction

Multiples and factors

Division by 1

The sieve works based on multiples and factors.

Explanation

The sieve works based on multiples and factors.

11) The sieve method is mainly used to identify:

Factors

Multiples

Prime numbers

Odd numbers

The sieve is mainly used to identify prime numbers.

Explanation

The sieve is mainly used to identify prime numbers.

12) In the sieve up to 30, which of these numbers will stay prime?

21

25

29

27

The number 29 stays prime when using the sieve up to 30.

Explanation

The number 29 stays prime when using the sieve up to 30.

13) Which of these numbers remains after using the sieve up to 30?

21

27

23

25

The number 23 remains prime up to 30.

Explanation

The number 23 remains prime up to 30.

14) Why don't we cross out the number 2 itself?

It is even

It is a factor of 4

It is prime

It is less than 10

We do not cross out 2 because it is prime.

Explanation

We do not cross out 2 because it is prime.

15) Which number would still remain uncrossed when using the sieve up to 20?

9

11

15

16

The number 11 remains uncrossed when using the sieve up to 20.

Explanation

The number 11 remains uncrossed when using the sieve up to 20.

16) When using the sieve, which number do we start crossing out first?

1

2

3

Multiples of 2

The sieve starts by crossing out multiples of 2 first.

Explanation

The sieve starts by crossing out multiples of 2 first.

17) If you cross out multiples of 2, 3, and 5 up to 50, what is the next prime left?

29

31

33

35

The next prime left after removing multiples of 2, 3, and 5 up to 50 is 31.

Explanation

The next prime left after removing multiples of 2, 3, and 5 up to 50 is 31.

18) If the sieve is extended to 100, which is the largest prime below 100?

97

99

91

The largest prime below 100 is 97.

Explanation

The largest prime below 100 is 97.

19) What is the output when eliminating multiples of 5?

10

12

14

15

When eliminating multiples of 5, the first number crossed out is 10.

Explanation

When eliminating multiples of 5, the first number crossed out is 10.

20) In the sieve, why do we stop crossing out at √n (square root of n)?

The sieve becomes too long

Multiples repeat after that

All composites are marked by then

Prime numbers stop existing

We stop at √n because beyond that, composites are already crossed out.

Explanation

We stop at √n because beyond that, composites are already crossed out.

Understanding the Sieve Method

1) In the sieve, why is 1 not considered a prime?

2) In the sieve, crossing out starts with 2, then 3, then 5, then:

3) When using the sieve up to 50, how many primes are found?

4) Which pattern do multiples of 3 make on the sieve?

5) Which prime is the first two-digit number?

6) The Sieve of Eratosthenes is used to:

7) After crossing out multiples of 2, which prime is used next?

8) When using the sieve up to 30, what is the next prime after 2 and 3?

9) What pattern do multiples of 2 make on the sieve?

10) The sieve is based on which mathematical property?

11) The sieve method is mainly used to identify:

12) In the sieve up to 30, which of these numbers will stay prime?

13) Which of these numbers remains after using the sieve up to 30?

14) Why don't we cross out the number 2 itself?

15) Which number would still remain uncrossed when using the sieve up to 20?

16) When using the sieve, which number do we start crossing out first?

17) If you cross out multiples of 2, 3, and 5 up to 50, what is the next prime left?

18) If the sieve is extended to 100, which is the largest prime below 100?

19) What is the output when eliminating multiples of 5?

20) In the sieve, why do we stop crossing out at √n (square root of n)?