SOLUTION: 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.

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Question 1017829: 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. 
How long would it be before the next time they cross the starting line again at the same time?
Found 2 solutions by Edwin McCravy, mathmate:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
1. a)A student says the prime factors of 17 are 1 and 17. Is 
the student correct?   Explain.
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.

b) List all the prime numbers between 10 and 20. Explain why 
they are  prime.  
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.

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

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. 
You didn't finish the question.  I will assume it should be 
something like this:

When will Shelby and Laura again be at the the starting line
at the same time, and how often?
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
Answer by mathmate(429)   (Show Source): You can put this solution on YOUR website!
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. 
How long would it be before the next time they cross the starting line again at the same time?

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
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