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In these lessons, we look into the Sieve of Eratosthenes and its use in finding prime numbers.

A **prime number** is a whole number that has exactly two factors, 1 and itself.

The **Sieve of Eratosthenes** is an ancient algorithm that can help us find all prime numbers
up to any given limit.

**How does the Sieve of Eratosthenes work?**

The following example illustrates how the Sieve of Eratosthenes can be used to find all the
prime numbers that are less than 100.

**Step 1:** Write the numbers 1 to 100 in ten rows.

**Step 2:** Cross out 1 because 1 is not a prime.

**Step 3:** Circle 2 and cross out all multiples of 2. (2, 4, 6, 8, 10, …)

**Step 4:** Circle 3 and cross out all multiples of 3. (3, 6, 9, 12, 15, …)

**Step 5:** Circle 5 and cross out all multiples of 5. (5, 10, 15, 20, …)

**Step 6:** Circle 7 and cross out all multiples of 7. (7, 14, 21, 28, …)

Circle all the numbers that are not crossed out and they are the prime numbers less than 100.

**How to use the Sieve of Eratosthenes to find all the prime numbers less than 100?**

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to
a specified integer. In this case we are using a chart up to 100.

**How to find all the prime numbers between 1 and 100 using the technique devised by the ancient Greek mathematician Eratosthenes?**

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
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