Triangle Puzzle

Add two straight lines to the figure and create 10 triangles.

Factors of numbers usually come in pairs. Thus, most numbers have an even number of factors.


Some special numbers, though, have an odd number of factors.

Find a copy of the chart below, in the folder at the computer desk. Under each number, list all the factors of the number.
Use pairing to help you find all of the factors.
Start with 1 for each number and end with the number itself, listing the factors in order.

When you are finished with all fifty numbers, circle all of the numbers (in the original typed list) that have exactly two factors.

What do we call this set of numbers? __________________

Put a square around all of the numbers (in the original typed list) that have an odd number of factors.

What do we call this set of numbers? __________________


One of the numbers, 18, is done for you, as an example.

Your work will be evaluated on neatness, accuracy, and answering the questions correctly.

Sieve of Eratosthenes - Can you follow the directions?

Find the file, on the computer desk, with copies of this chart.

Definition: A prime number has exactly 2 factors, 1 and itself.

1 is not a prime number, because it only has one factor, itself.
Cross out the number one, because it is not prime.

2 is the first prime number, and the only even prime number.
Circle 2, because it is prime.
Cross out all of the rest of the even numbers. They are not prime.

Why? ________________________________________

Now, 3 is the first number, in the list, that is neither crossed out or circled.
Circle the number 3. It is the second prime number.
Continue by crossing out all of the rest of the numbers that are divisible by three.
You can do this by remembering your 3 times tables, or just by counting every third number.

What is the first number in your list that is neither circled or crossed out? ________
Circle it and then cross out all of the numbers that have that number as a factor.
You should notice that all of these numbers are in the same two columns.

Continue by circling the first number, in your list, that is not already crossed out or circled. Then, cross out all of the rest of the numbers that are divisible by that number.

When you are done with that, circle all of the rest of the numbers, in the list, that are neither crossed out nor circled.

Finally, make a list of the circled numbers. If you have followed the directions exactly, there should be 25 numbers in your list.

There should be 5 numbers that end in 1.
There should be only 1 even number.
There should be 7 numbers that end in 3, but only one that ends in 5.
There should be 6 numbers that end in 7 and 5 numbers that end in 9.

There are no numbers, in your list, that end in 4, 6, 8, or 0.