Draw a number line and show all the numbers that
… are between 1 and 20 and have exactly 4 factors
What are those numbers? Which ones have exactly 4 factors?
To determine the numbers between 1 and 20 that have exactly 4 factors, we can start by understanding what a factor is. A factor of a number is a number that divides evenly into it without leaving any remainder.
To draw the number line, start by listing the numbers from 1 to 20:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Now, let's identify the numbers with exactly 4 factors.
For a number to have exactly 4 factors, it needs to be either a perfect square or the product of two distinct prime numbers.
Let's mark the perfect squares on the number line first:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
We can see that the numbers 1, 4, 9, and 16 are perfect squares.
Next, let's mark the numbers that are the product of two distinct prime numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
We can see that the numbers 6 (2 * 3), 10 (2 * 5), 14 (2 * 7), and 15 (3 * 5) are the product of two distinct prime numbers.
So, the numbers between 1 and 20 that have exactly 4 factors are: 4, 9, 15, and 16.
Here's the final number line:
1 2 3 [4] 5 6 7 8 [9] 10 11 12 13 14 [15] 16 17 18 19 20
The numbers in brackets [ ] are the ones that have exactly 4 factors.