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

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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.

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.

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