If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution.  If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

025.  `query 25

Question:  `q query 5.3.12  using prime factors find the greatest common factor of 180 and 300.

What is the greatest common factor and how did you use prime factors to find it?

Your solution: 

Confidence Assessment:

Given Solution: 

`a** The prime factorizations are 180=2 ^2 * 3 ^ 2 * 5  and 300=2 ^2 * 3 ^1 * 5^2.

They have in commin 2^2, 3 and 5, and no higher power of any of these factors.  Since  2^2 * 3^1 * 5^1=60 the greatest common factor is 60. **

Self-critique (if necessary):

Self-critique Rating:

Question:  `q query 5.3.24  Euclidean algorithm to find GCF(25,70)

 Show how you used the Euclidean algorithm to find the greatest common factor of the two numbers.

Your solution: 

Confidence Assessment:

Given Solution: 

`a** To apply the Euclidean algorithm we divide the larger number by the smaller, obtaining a remainder.  We then divide the remainder by the divisor and repeat this process until we get 0 remainder.  The greatest common divisor is the last divisor.

In this case 70 divided by 25 gives us remainder 20.        

Then we divide the previous divisor 25 by the remainder 20, obtaining remainder 5.

Then we divide the previous divisor, which is now 20, by the remainder 5.  The remainder of this division is 0.

So the last divisor, which is 5, is the greatest common factor. **

Self-critique (if necessary):

Self-critique Rating:

Question:  `q query 5.3.36  LCM of 24, 36, 48 

How did you use the prime factors of the given numbers to find their greatest common factor?

Your solution: 

Confidence Assessment:

Given Solution: 

`a** The prime factorizations are 24 = 2*2*2*3, 36 = 2*2*3*3, 48 = 2*2*2*2*3.

The smallest number that includes all these factors has four 2's and two 3's.

2*2*2*2 * 3*3 = 144.  So 144 is the GCF. **

Self-critique (if necessary):

Self-critique Rating:

Question:  `q query 5.3.48 GCF of 48, 315, 450

Show how you used the Euclidean algorithm to find the greatest common factor of the three given numbers.

Your solution: 

Confidence Assessment:

Given Solution: 

`a** Applying the Euclidean Algorithm to 315 and 48:

315 divided by 48 gives us remainder 27. 

48 divided by 27 gives us remainder  21. 

27 divided by 21 gives us remainder 3.

 6 divided by 3 gives us remainder 0. 

The last divisor is 3, which is therefore the GCF of 315 and 48. 

The GCF of the three numbers is therefore the GCF of 450 and 3, which is found by first dividing 450 by 3, which gives us remainder 0. 

So the last divisor is 3, which is therefore the GCF of the three numbers.  **

 Query   Add comments on any surprises or insights you experienced as a result of this assignment.