Sieve of Eratosthenes
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Over 2,000 years ago, a Greek mathematician named Eratosthenes created a system for
finding prime numbers.
A prime number is a whole number that has only two factors, itself and one.
1 is not a prime number since it only has one factor.
All other numbers that have more than two factors are called composite numbers.
You can use Eratosthene’s Sieve (a sieve separates things out) to find all of the prime
numbers less than 100. Follow these directions:
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First, cross out 1.
Circle the prime numbers 2, 3, 5, and 7.
Next, use a red pencil to cross out all the multiples of 2 with a red l.
Then use blue pencil and cross out the multiples of 3 with a blue ―.
Using green, cross out multiples of 5 with a green /.
Try a purple \ for multiples of 7.
(Do you start to notice patterns as you cross out multiples?)
Do NOT
cross out 2
Name ___________________________ Date ___________________ # ________
When you are finished, circle all of the numbers that have NOT been crossed out.
These numbers are prime.
List all of the prime numbers that are less than 100 (there are 25):
____ ____ ____ ____ ____ ____ ____ ____ ____ ____
____ ____ ____ ____ ____ ____ ____ ____ ____ ____
____ ____ ____ ____ ____
How many even primes are there?
What do you know about numbers that have more than one slash?
For example, 30 should have a red line, blue line, and green line. What are these
numbers called?
Which of the following is a composite number: 37, 47, 57, 67?
Extensions (optional):
Make your own grid for the numbers 101-200. Find all of the prime numbers. Is the
number of primes on this grid the same as on the hundred grid?