Sieve of Eratosthenes Quiz: Explore How Prime Numbers Are Found

  • 4th Grade
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| Questions: 20 | Updated: Dec 15, 2025
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1) Which pattern do multiples of 3 make on the sieve?

Explanation

Multiples of 3 appear every 3rd number: 3,6,9,12,…

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About This Quiz
Sieve Of Eratosthenes Quizzes & Trivia

Step into prime hunting with a simple, clever idea. This quiz walks you through the Sieve of Eratosthenes and shows how crossing out multiples brings the prime numbers into view. It’s an easy way to see how this old method still helps us understand number patterns today. Try it out... see moreand see how smoothly you can use the sieve! see less

2) How many primes are there between 31 and 50? __

Explanation

31,37,41,43,47 → 5 primes.

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3) There are fewer primes in higher ranges because primes stop appearing.

Explanation

Primes never stop; they become less frequent as numbers increase because more numbers are composites of smaller primes.

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4) Which prime comes directly after 59?

Explanation

60 even, 61 not divisible by 2,3,5,7 → prime → comes after 59.

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5) The Sieve of Eratosthenes is used to:

Explanation

The sieve systematically finds all primes up to a limit n by marking multiples of each found prime. Numbers never marked are primes. It simplifies prime finding by using elimination rather than checking each number individually.

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

Explanation

We keep 2 since it's prime. The first numbers crossed are multiples of 2 (4,6,8,…), as all even numbers greater than 2 are composite.

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7) We cross out the number 2 in the sieve.

Explanation

2 is the first prime, so we keep it. Only its multiples are crossed.

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

Explanation

After removing even numbers, 3 is the smallest uncrossed number, making it the next prime. We then cross out multiples of 3.

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9) Why do we stop crossing out at √n (square root of n)?

Explanation

Every composite number ≤ n has at least one prime factor ≤ √n. So after handling primes ≤ √n, all composites are already marked.

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

Explanation

9=3×3, so it’s a multiple of 3 and must be crossed.

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11) The numbers left uncrossed after applying the sieve are all prime numbers.

Explanation

Each composite number is removed as a multiple of a smaller prime. Remaining numbers are prime.

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12) The sieve method is based on which mathematical property?

Explanation

The sieve relies on multiples and factors — crossing out all multiples of smaller primes to reveal primes.

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13) Which of these numbers remain unmarked (prime) after crossing multiples of 2,3, and 5 up to 30?

Explanation

15=3×5 is crossed; 7,11,13,17 are not divisible by 2,3,5 and remain unmarked (prime).

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

Explanation

9=3×3, 15=3×5, 16 even, all crossed. 11 has no small divisors, so remains uncrossed.

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15) Which of these is not a prime number?

Explanation

49=7×7, not prime; others have no small divisors and are primes.

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16) Which of the following are primes between 1 and 30?

Explanation

All except 9 (3×3) are primes in this range.

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17) Which numbers are crossed out when removing multiples of 7 up to 50?

Explanation

All are multiples of 7 → crossed out during the 7-pass.

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18) In the sieve up to 30, the next prime after 2 and 3 is __.

Explanation

After removing multiples of 2 and 3, the next uncrossed number is 5, which is prime.

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19) The pattern for multiples of 2 is that every __ number is crossed out.

Explanation

Even numbers occur every 2 steps → every second number is crossed.

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20) The largest prime less than 50 is __.

Explanation

Checking down from 50: 50 even, 49=7×7, 48 even → 47 prime → largest below 50.

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Which pattern do multiples of 3 make on the sieve?
How many primes are there between 31 and 50? __
There are fewer primes in higher ranges because primes stop appearing.
Which prime comes directly after 59?
The Sieve of Eratosthenes is used to:
When using the sieve, which number do we start crossing out first?
We cross out the number 2 in the sieve.
After crossing out multiples of 2, which prime is used next?
Why do we stop crossing out at √n (square root of n)?
You cross out 9 because it is a multiple of 3.
The numbers left uncrossed after applying the sieve are all prime...
The sieve method is based on which mathematical property?
Which of these numbers remain unmarked (prime) after crossing...
Which number would still remain uncrossed when using the sieve up to...
Which of these is not a prime number?
Which of the following are primes between 1 and 30?
Which numbers are crossed out when removing multiples of 7 up to 50?
In the sieve up to 30, the next prime after 2 and 3 is __.
The pattern for multiples of 2 is that every __ number is crossed out.
The largest prime less than 50 is __.
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