Applying the Sieve to Numbers

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| Questions: 20 | Updated: Nov 26, 2025
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1) Which numbers remain prime between 1 and 20 after applying the sieve?

Explanation

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

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About This Quiz
Applying The Sieve To Numbers - Quiz

Ready to put the sieve to the test? In this quiz, you’ll practice crossing out multiples, spotting which numbers remain prime, and noticing patterns as the list gets smaller. We bring you this quiz to challenge your number sense and show how quickly the sieve reveals all the primes.

2) Which prime factorization is correct for 15?

Explanation

The prime factorization of 15 is 3 × 5.

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

Explanation

The primes between 30 and 40 are 31 and 37.

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

Explanation

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

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

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

Explanation

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

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6) Which of these numbers is prime?

Explanation

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

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

Explanation

The largest prime below 50 is 47.

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8) Which prime is the largest below 20?

Explanation

The largest prime below 20 is 19.

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

Explanation

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

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10) Which prime comes directly after 11?

Explanation

The prime number directly after 11 is 13.

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11) Which number is prime between 40 and 50?

Explanation

The number 43 is prime between 40 and 50.

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

Explanation

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

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13) Which of these numbers is composite?

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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17) Which prime number comes directly after 37?

Explanation

The prime number after 37 is 41.

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18) Which prime number follows 23?

Explanation

The prime number that follows 23 is 31.

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19) Which of these is not prime?

Explanation

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

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

Explanation

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

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Which numbers remain prime between 1 and 20 after applying the sieve?
Which prime factorization is correct for 15?
Which prime numbers remain between 30–40 using the sieve?
What happens when multiples of 7 are crossed out up to 50?
When crossing out multiples of 3, which of these numbers is...
Which of these numbers is prime?
If you extend the sieve to 50, which is the largest prime below 50?
Which prime is the largest below 20?
Which number gets crossed out when removing multiples of 3?
Which prime comes directly after 11?
Which number is prime between 40 and 50?
If we cross out multiples of 2, 3, and 5, which number between...
Which of these numbers is composite?
Which pattern of numbers stays when all multiples are crossed out?
If the sieve is used up to 30, how many primes remain?
Which number is crossed out first when removing multiples of 11 up to...
Which prime number comes directly after 37?
Which prime number follows 23?
Which of these is not prime?
When crossing out multiples of 2, which number disappears first?
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