# Sieve of Eratosthenes: Lesson for Kids

Instructor: Nick Rogers
Prime numbers are important to mathematicians, and there are many ways to find them. The sieve of Eratosthenes is one of the first that was ever developed, which you'll explore here.

## Eratosthenes and His Sieve

Eratosthenes was a Greek scientist who lived nearly 2,000 years ago, studied geography, and made some of the first maps of the entire known world. He is credited with inventing a method for finding prime numbers known as a sieve. Lets review some information about factors and prime numbers that can help us understand his sieve.

## Factors

Numbers are made up of other numbers called factors. We can think of factors as the building blocks of a number. Consider the number 12, which can be written as 3 x 4, or 6 x 2, or 12 x 1. The factors of 12 are 1, 2, 3, 4, 6, and 12. Numbers always have themselves and '1' as factors since any number can be written as itself times 1.

One reason that it is useful to break a number into its factors is because it makes multiplication easier. If we multiply 12 x 36, we can use the fact that 12 = 3 x 4, 36 = 6 x 6, and 6 = 3 x 2 to see that:

• 12 x 36 = (3 x 4) x (6 x 6)
• 12 x 36 = 3 x 4 x 3 x 2 x 3 x 2

Do you see how we've just written a complicated multiplication problem as many small problems? This is one of the benefits of factoring.

## Prime Numbers

Prime numbers are numbers that can be divided cleanly by only themselves and 1. The first few prime numbers are 2, 3, 5, and 7. Can you find some more? Prime numbers are the essential building blocks of all numbers.

If we try to break apart the multiplication problem 7 x 13 as we did above, we will not be able to. This is because 7 and 13 are both prime numbers. There is no way to simplify them any further. In fact, any number can always be written as a product of primes. Why not try some out for yourself?

## How the Sieve Works

Sieves or 'sifters' are typically used for separating solid materials from liquids. They usually have a metal mesh, and you may have seen one in a kitchen. The sieve of Eratosthenes works in much the same way - except instead of pouring liquid through it, you pour numbers. In order to apply the sieve, just follow these simple steps:

1. Begin with a large set of numbers that you would like to remove non-primes from, and put them in order.

2. Take the first non-prime that you find (such as 2), and remove all of the multiples of that number from the set ( 4, 6, 8...).

3. Repeat the second step with the next prime number.

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