Sieve Comparison Quiz: Test Your Knowledge On Different Sieve Ranges

1) What is the first number you circle (keep) in the sieve?

1

2

3

4

The Sieve of Eratosthenes starts with the smallest prime, which is 2. We circle 2 and cross out all its multiples (4, 6, 8, …). 1 is not prime, so we don’t circle it. Step-by-step: Start at 2 → circle it. So first circled number = 2.

Explanation

The Sieve of Eratosthenes starts with the smallest prime, which is 2. We circle 2 and cross out all its multiples (4, 6, 8, …). 1 is not prime, so we don’t circle it. Step-by-step: Start at 2 → circle it. So first circled number = 2.

2) You cross out 9 because it is a multiple of 3.

True

False

After crossing multiples of 2, go to next uncrossed number: 3. Circle 3, then cross out multiples of 3 starting from 3×3=9 → So yes, 9 is crossed out because 9=3×3.

Explanation

After crossing multiples of 2, go to next uncrossed number: 3. Circle 3, then cross out multiples of 3 starting from 3×3=9 → So yes, 9 is crossed out because 9=3×3.

3) After 2,3,5, the next number you use to cross out multiples is:

6

7

9

11

After crossing multiples of 2,3,5, next unmarked number after 5 is 7 (6 is crossed as 2×3). Circle 7, then cross out multiples starting at 7×7=49.

Explanation

After crossing multiples of 2,3,5, next unmarked number after 5 is 7 (6 is crossed as 2×3). Circle 7, then cross out multiples starting at 7×7=49.

4) How many numbers between 31 and 50 are crossed out as multiples of 2,3,5,7?

12

14

15

16

Total 31–50=20 numbers. Primes in range:31,37,41,43,47 (5). Composites=20–5=15 → 15 crossed out.

Explanation

Total 31–50=20 numbers. Primes in range:31,37,41,43,47 (5). Composites=20–5=15 → 15 crossed out.

5) Which statement is true?

Half of the numbers up to 30 are prime.

There are fewer primes above 30 than below 30.

1–50 has exactly double the primes of 1–30.

First:10/30=1/3 not half→False. Second:Primes≤30=10,31–50=5→5

Explanation

First:10/30=1/3 not half→False. Second:Primes≤30=10,31–50=5→5

6) Which numbers do you cross out first? (Select all)

2

4

6

8

10

We circle 2 and cross out all multiples of 2 greater than 2: 2×2=4, 2×3=6, 2×4=8, 2×5=10 → So we cross out 4,6,8,10. We keep 2 (don’t cross it).

Explanation

We circle 2 and cross out all multiples of 2 greater than 2: 2×2=4, 2×3=6, 2×4=8, 2×5=10 → So we cross out 4,6,8,10. We keep 2 (don’t cross it).

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7) How many multiples of 5 (greater than 5) are in 1–30?

4

5

6

7

Multiples of 5 greater than 5 up to 30: 10,15,20,25,30 → Count=5. We don’t count 5 itself—only numbers to cross out.

Explanation

Multiples of 5 greater than 5 up to 30: 10,15,20,25,30 → Count=5. We don’t count 5 itself—only numbers to cross out.

8) Which of these are primes left after crossing multiples of 2,3,5?

7

11

13

15

17

After crossing multiples of 2→4,6,8,…; multiples of 3→9,12,15,…; multiples of 5→10,15,20,… check: 7,11,13,17 are not divisible by 2,3,5; 15=3×5→crossed.

Explanation

After crossing multiples of 2→4,6,8,…; multiples of 3→9,12,15,…; multiples of 5→10,15,20,… check: 7,11,13,17 are not divisible by 2,3,5; 15=3×5→crossed.

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9) 1 is a prime number.

True

False

A prime number has exactly two different factors: 1 and itself. 1 has only one factor (1). So 1 is not prime.

Explanation

A prime number has exactly two different factors: 1 and itself. 1 has only one factor (1). So 1 is not prime.

10) Cross out multiples of 7 starting from 14. Which are correct?

14

21

28

35

42

Multiples of 7 starting from 14: 7×2=14,7×3=21,7×4=28,7×5=35,7×6=42 → All correct.

Explanation

Multiples of 7 starting from 14: 7×2=14,7×3=21,7×4=28,7×5=35,7×6=42 → All correct.

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11) 49 is crossed out because it is 7×7.

True

False

When we reach 7, we cross out multiples starting at 7×7=49. Smaller multiples already crossed by 2 or 3. 49=7×7 so it’s crossed out.

Explanation

When we reach 7, we cross out multiples starting at 7×7=49. Smaller multiples already crossed by 2 or 3. 49=7×7 so it’s crossed out.

12) Which numbers between 40 and 50 are still unmarked after crossing 2,3,5,7?

41

43

45

47

49

41,43,47 not divisible by 2,3,5,7 → primes. 45=5×9,49=7×7 → crossed.

Explanation

41,43,47 not divisible by 2,3,5,7 → primes. 45=5×9,49=7×7 → crossed.

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13) How many more primes are in 1–50 than in 1–30?

3

4

5

6

Primes in 1–30=10, in 1–50=15. Difference=15−10=5.

Explanation

Primes in 1–30=10, in 1–50=15. Difference=15−10=5.

14) There are more composite numbers in 1–50 than in 1–30.

True

False

1–30:30 numbers→10 primes→20 composites. 1–50:50 numbers→15 primes→35 composites → 35>20 → True.

Explanation

1–30:30 numbers→10 primes→20 composites. 1–50:50 numbers→15 primes→35 composites → 35>20 → True.

15) Why are there fewer primes in higher ranges?

More numbers to check

More multiples to cross out

Primes get smaller

The sieve stops working

As numbers get larger, there are more small primes (2,3,5,7,…) so more multiples to cross out. Hence fewer numbers left uncrossed (fewer primes). Example: 1–10→4 primes; 41–50→3 primes.

Explanation

As numbers get larger, there are more small primes (2,3,5,7,…) so more multiples to cross out. Hence fewer numbers left uncrossed (fewer primes). Example: 1–10→4 primes; 41–50→3 primes.

16) After crossing multiples of 2 and 3, the smallest number still unmarked (besides 2 and 3) is __.

List numbers 1–10 after crossing multiples of 2 and 3: Crossed: 2,4,6,8,10 (multiples of 2); Crossed: 3,6,9 (multiples of 3); Still unmarked: 1,5,7 but 1 is not prime → Smallest unmarked after 3 = 5.

Explanation

List numbers 1–10 after crossing multiples of 2 and 3: Crossed: 2,4,6,8,10 (multiples of 2); Crossed: 3,6,9 (multiples of 3); Still unmarked: 1,5,7 but 1 is not prime → Smallest unmarked after 3 = 5.

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18) The largest prime less than 50 is __.

Check numbers near 50: 49=7×7 not prime, 48 even not prime, 47 not divisible by 2,3,5,7 → prime. So largest

Explanation

Check numbers near 50: 49=7×7 not prime, 48 even not prime, 47 not divisible by 2,3,5,7 → prime. So largest

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Sieve Comparison Quiz: Test Your Knowledge on Different Sieve Ranges