Question 1017829
Question:
1. a)A student says the prime factors of 17 are 1 and 17. Is the student correct?   Explain.
b)  List all the prime numbers between 10 and 20. Explain why they are  prime.  

2. State the numbers that are neither prime, nor composite. Explain. 

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.  
<i>How long would it be before the next time they cross the starting line again at the same time?</i>
 
Solution:
1(a) Incorrect.  1 is neither prime nor composite.
She could say 17 is divisible by only 1 or 17, or the factors of 17 are 1 and 17.
(b) 11,13,17,19
These are numbers between 10 and 20 that have factors 1 and the number itself, which is the definition of primes.
 
2. There are quite a few of them:
A. The first prime number starts with 2, and upwards.  So all numbers below 2 are not primes.  0 is not a prime, it cannot be a factor of any other number. 1 is not a prime, it is a factor of all integers.  Negative numbers are not primes.  The positive equivalents can do a "better job".
B. All numbers that are not integers are not primes.  1.1 cannot be a prime, nor 45/37.
C. All complex numbers are not primes.  A prime must be a positive real integer greater than or equal to 2.
(read reference below for a more detailed explanation)
 
3. We need to find the LCM of 30 and 40 to find the least time before they meet again at the starting point.
For this problem, an easy way to find the LCM is to first find the HCF, which is 10*.  The LCM is 30*40/10=120.  So in 120 seconds, they will meet again at the starting point.

* Here we used the Euclid's algorithm to find the HCF, which is to take the difference between the two numbers.  If the difference divides both numbers, it is the HCF.  If not, repeat using the difference and the smaller number until it does.
Since 40-30=10 divides both 30 and 40, 10 is the HCF.
Example: Find HCF of 24 and 42
42-24=18  doesn't divide either
24-18=6   divides both 24 and 18.
So 6 is the HCF of 42 and 24.
 
Reference:
http://mathforum.org/library/drmath/view/55940.html