Question 1017829
1. a)A student says the prime factors of 17 are 1 and 17. Is 
the student correct?   Explain.
<pre>
No, the only prime factor of 17 is 17 itself.  1 is not a 
prime number because it has only (exactly) one prime factor, 
which is 1 itself.  A prime number has exactly two factors. 
</pre>
b)  List all the prime numbers between 10 and 20. Explain why 
they are  prime.  
<pre>
11, 13, 17, 19

11 is prime because it has exactly 2 factors, 1 and 11.
13 is prime because it has exactly 2 factors, 1 and 13.
17 is prime because it has exactly 2 factors, 1 and 17.
19 is prime because it has exactly 2 factors, 1 and 19. 
</pre>
2. State the numbers that are neither prime, nor composite. 
Explain. 
<pre>
There is only one such integer, 1.  A prime number must 
have exactly two factors.  A composite number must have 
more than two factors. The number 1 does not fit either 
category because it has exactly one factor, itself.   
</pre>
3. Shelby completes one lap of a go­cart track every 40 seconds.
Laura completes one lap of the same track every 30 seconds. 
Suppose Shelby and Laura cross the starting line at the same time. 
<pre>
You didn't finish the question.  I will assume it should be 
something like this:
</pre>
When will Shelby and Laura again be at the the starting line 
at the same time, and how often?
<pre>
They will be at the starting line at the same time when they have
each completed a whole number of laps.  That will be at the common
multiples of 40 and 30 seconds. The least common multiple of 40
and 30 is 120.  So they will be together at the starting every
120 seconds or every 2 minutes.

Edwin</pre>