Understanding the Sieve Method

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| Questions: 20 | Updated: Nov 26, 2025
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1) The Sieve of Eratosthenes is used to:

Explanation

The Sieve of Eratosthenes is used to find prime numbers.

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About This Quiz
Understanding The Sieve Method - Quiz

Can you outsmart the sieve and find the hidden primes before it does? In this quiz, you’ll explore the Sieve of Eratosthenes, a clever method that crosses out multiples to reveal primes hiding in the number grid. Take this quiz and see how this ancient trick still makes finding primes... see morefun and easy today!
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2) After crossing out multiples of 2, which prime is used next?

Explanation

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

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

Explanation

The next prime after 2 and 3 is 5.

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

Explanation

Multiples of 2 form the pattern of every second number.

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

Explanation

Multiples of 3 form the pattern of every third number.

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

Explanation

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

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

Explanation

The number 23 remains prime up to 30.

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8) The sieve is based on which mathematical property?

Explanation

The sieve works based on multiples and factors.

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

Explanation

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

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

Explanation

The first two-digit prime number is 11.

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

Explanation

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

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12) The sieve method is mainly used to identify:

Explanation

The sieve is mainly used to identify prime numbers.

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

Explanation

The sieve starts by crossing out multiples of 2 first.

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

Explanation

We do not cross out 2 because it is prime.

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

The largest prime below 100 is 97.

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

Explanation

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

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The Sieve of Eratosthenes is used to:
After crossing out multiples of 2, which prime is used next?
When using the sieve up to 30, what is the next prime after 2 and 3?
What pattern do multiples of 2 make on the sieve?
Which pattern do multiples of 3 make on the sieve?
In the sieve, why is 1 not considered a prime?
Which of these numbers remains after using the sieve up to 30?
The sieve is based on which mathematical property?
In the sieve, crossing out starts with 2, then 3, then 5, then:
Which prime is the first two-digit number?
When using the sieve up to 50, how many primes are found?
The sieve method is mainly used to identify:
When using the sieve, which number do we start crossing out first?
Why don't we cross out the number 2 itself?
In the sieve, why do we stop crossing out at √n (square root of...
If you cross out multiples of 2, 3, and 5 up to 50, what is the next...
Which number would still remain uncrossed when using the sieve up to...
In the sieve up to 30, which of these numbers will stay prime?
If the sieve is extended to 100, which is the largest prime below 100?
What is the output when eliminating multiples of 5?
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