Prime numbers are useful for simplifying or reducing fractions, prime factorization, and finding the lowest common denominator. Here’s a way an activity to help students find prime numbers without relying on only memory.

The method comes from the Greek Mathematician, Eratoshenes, who lived about two thousand years ago. It’s called The Sieve of Eratoshenes. A sieve is similar to a colander that you may use to rinse rice or pasta. The water drains and the rice remains in the colander. Likewise, I will give some background and explain how to use the Sieve of Eratoshenes to eliminate composite numbers and to determine the prime numbers between 1 and 100. Then, share a few online resources. First, you’ll need a hundreds chart and at least one colored pencil. Once the process is complete, twenty-five prime numbers should remain unmarked.

On the hundred chart, cross out “1” because it’s neither prime nor composite. Next circle “2” since it’s has only two factors. Then, place an “x” on all multiples of two. For example, 2, 4, 6, 8, 10, 12. 14 … etc. Remember, if a number is a multiple of another number, it has more than two factors and is not considered a prime number. The next number unmarked is three. Circle it. Then, place an “x” on all multiples of three. It’s a good idea to use a different colored pencil. It is easier to backtrack if needed. Next, repeat the process for “5” and “7” which will be the end of the first row. That’s it!

All of the unmarked remaining numbers are prime numbers. There should be a total of twenty-five. They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.