Interactive Sieve of Eratosthenes

What the sieve does

A prime number has exactly two factors: 1 and itself. The Sieve of Eratosthenes, named after a Greek mathematician who lived over 2,000 years ago, finds primes by elimination. Circle 2 and cross out every other multiple of 2. Circle the next number left, 3, and cross out its multiples. Keep going, and the numbers that never get crossed out are the primes.

On this page, Cross out 1 starts things off. Each Multiples of button circles that prime and crosses out its multiples in its own color: yellow for 2, green for 3, blue for 5 and pink for 7. A square keeps the color of the first prime that crossed it out. Auto step does the next step for you. With Cross out by hand on, the child taps the multiples themselves. When 2, 3, 5 and 7 are done, Circle the primes rings the 25 primes.

Why stop at 7?

Every number up to 100 that is not prime can be written as a product of two smaller numbers, and the smaller of the two is at most 10, because 11 × 11 = 121 is already over 100. So every composite number up to 100 has a factor of 2, 3, 5 or 7 and gets crossed out by one of them. Working this out is good reasoning practice for older students.

Common mix-ups

• Thinking 1 is prime. It has only one factor, so it is neither prime nor composite.
• Thinking all odd numbers are prime. 9, 15, 21 and 91 are odd but crossed out.
• Thinking 2 isn't prime because it is even. It is the only even prime: its factors are just 1 and 2.
• Assuming 51 or 57 must be prime because they look it. Tap them after the 3s: 51 = 3 × 17 and 57 = 3 × 19.

A 10-minute sieve

• Turn on Cross out by hand. Cross out 1 and ask the child why it goes first.
• Press Multiples of 2 and have the child tap the even numbers. Ask what the crossed squares look like.
• Do the 3s by hand. Many of their multiples are already yellow; talk about why 6, 12 and 18 were crossed out twice.
• Press Auto step for the 5s and then the 7s while the child predicts which new squares will be colored.
• Press Circle the primes and ask the child to list the primes between 1 and 20 from memory.

Where it fits by grade

• Grade 4: decide whether a number up to 100 is prime or composite, and find factors and multiples (4.OA.B.4). In England, Year 5 pupils work out whether a number up to 100 is prime and recall primes up to 19.
• Grades 5 and 6: prime numbers underpin prime factorization, greatest common factors and least common multiples. In England, Year 6 pupils identify common factors, common multiples and primes.

Learning more

Times tables and factors are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. When a question about primes is tricky, the AI tutor asks guiding questions so the student does the reasoning.