Assignment 25

course Mth 151

???a??g??N?????assignment #025

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025. `query 25

College Algebra

04-13-2007

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18:07:03

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?

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RESPONSE -->

180/2 = 90

90/2 = 45

45/3 = 15

15/3 = 5

180 = 2^2 * 3^2 * 5

300/2 = 150

150/2 = 75

75/3 = 25

25/5 = 5

5/5 = 1

300 = 2^2 * 3 * 5^2

2^2 * 3 * 5 = 60

confidence assessment: 3

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18:07:41

** 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. **

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RESPONSE -->

Ok.

self critique assessment: 3

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18:11:25

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.

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RESPONSE -->

70/25 = remainder 20

25/20 = remainder 5

20/5 = remainder 0

GCF is 5

confidence assessment: 3

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18:12:22

** 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. **

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RESPONSE -->

Ok.

self critique assessment: 3

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18:14:22

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?

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RESPONSE -->

24/2 = 12

12/2 = 6

6/2 = 3

3/3 = 1

24 = 2^3 * 3

36/2 = 18

18/2 = 9

9/3 = 3

3/3 = 1

36 = 2^2 * 3^2

48/2 = 24

24/2 = 12

12/2 = 6

6/2 = 3

3/3 = 1

48 = 2^4 * 3

2^4 * 3^2 = 144

confidence assessment: 3

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18:14:49

** 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. **

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RESPONSE -->

Ok.

self critique assessment: 3

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18:20:26

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.

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RESPONSE -->

315/48 = remainder 27

48/27 = remainder 21

27/21 = remainder 6

21/6 = remainder 3

6/3 = remainder 0

GCF of 48 and 315 = 3

450/3 = remainder 0

GCF of 48, 315, 450 = 3

confidence assessment: 3

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18:20:53

** 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. **

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RESPONSE -->

Ok.

self critique assessment: 3

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18:22:22

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

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RESPONSE -->

It seems like it was easier to learn these methods here than it was in high school.

self critique assessment: 3

It's always easier the second time around. Also, in high school teaching is aimed at the SOL and often requires shortcuts as opposed to understanding.

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Good work. Let me know if you have questions.