A prime number is an integer that
cannot be evenly divided by any other integer except 1 and itself. In
other words, a prime number has no other factors except 1 and itself.
For example, 7 can only be evenly divided by 1 and 7, so we say that
it is a prime number. (By the way, all prime numbers must have exactly
two
factors so by definition 1 is not a prime number since its only factor
is 1.)
Ask the students how we can test which
numbers are prime using ChartWorld.
Let's start with the number 2. We are
not allowed to click on the number 1 nor the number 2, so 2 must be a
prime number.
How about 3? Since we aren't allowed
to click on 1 or 3, the only number we can click on is 2.
Notice that after we clicked on 2, the
number 3 is not colored,
therefore it is also a prime number.
Moving to the next number, we see
that 4 is already colored because 2 is a factor of 4. This means that
the number 4 is not a prime number. Instead the number 4 is called a composite
number, which means that it has more than two factors (in this case 1
and 4, as well as 2).
The next number to check is 5. The numbers 2
and 4 are
already colored, so let's click on 3 (be sure to change the ink
color using the F12 key for each number).
After clicking on 3, the number 5 is still not colored.
This means that it is a prime number.
How about the number 6? Notice that is
is colored in both orange and blue. This means that it is a
composite number with the factors 2 and 3, as well as 1 and 6. In
fact, all of the "stacked" numbers (colored in both orange
and blue  12, 18, 24, etc.) are multiples of 6.
Up to this point, we have determined
that the numbers 2, 3, and 5 are prime numbers and the numbers 4
and 6 are composite numbers. Let's
continue on to the number 7. Remember, we cannot click on the number
1, so let's click on the only blank number less than 7. Click on the
number 5. Notice
that 7 is still not colored, so 7 must also be a prime number. Also
notice that the number 30 is "stacked" with the colors
orange, blue, and green. This is because 2 x 3 x 5 = 30. The multiples
of 30 have all three colors. Finally,
let's click on the number 7 to find the rest of the composite numbers. The
prime numbers under 100 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.
With some programming to ChartWorld,
we can also show the prime numbers like this... Notice
that all of the prime numbers are in white this time and that the
number 1 is colored in black.
