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Mrrafil [7]
3 years ago
8

Problem Set

Mathematics
1 answer:
Naddik [55]3 years ago
6 0

a) (15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3

b) The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)

c) (2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

<em><u>Solution:</u></em>

Given that,

Use the set of ordered pairs below to answer each question.

{(4, 20),  (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}

<h3>a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3</h3>

So we must find GCF of the ordered pairs

GCF of 4 and 20:

The factors of 4 are: 1, 2, 4

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4

GCF of 8 and 4:

The factors of 4 are: 1, 2, 4

The factors of 8 are: 1, 2, 4, 8

Then the greatest common factor is 4

GCF of 2 and 3:

The factors of 2 are: 1, 2

The factors of 3 are: 1, 3

Then the greatest common factor is 1

<em><u>GCF of 15 and 3:</u></em>

The factors of 3 are: 1, 3

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3

<em><u>GCF of 6 and 15:</u></em>

The factors of 6 are: 1, 2, 3, 6

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3

GCF of 6 and 30:

The factors of 6 are: 1, 2, 3, 6

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6

GCF of 1 and 5:

The factors of 1 are: 1

The factors of 5 are: 1, 5

Then the greatest common factor is 1

GCF of 6 and 18:

The factors of 6 are: 1, 2, 3, 6

The factors of 18 are: 1, 2, 3, 6, 9, 18

Then the greatest common factor is 6

<em><u>GCF of 0 and 3:</u></em>

The factors of 0 are: All Whole Numbers

The factors of 3 are: 1, 3

Then the greatest common factor is 3

Summarizing the results:

(15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3

<h3>b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.</h3>

So let us find the factors of second cordinate and check

<em><u>For (4, 20) , the factors of 20 are 1, 2, 4, 5, 10, 20</u></em>

Thus first coordinate 4 is factor of second cordinate

<em><u>For (8, 4) the factors of 4 are 1, 2, 4</u></em>

Thus first coordinate is not a factor of second cordinate

<em><u>For (2, 3), the factors of 3 are 1, 3</u></em>

Thus first coordinate is not a factor of second cordinate

<em><u>For (15, 3), the factors of 3 are 1 and 3</u></em>

Thus first coordinate is not a factor of second cordinate

<em><u>For (6, 15) , the factors of 15 are 1, 3, 5, 15</u></em>

Thus first coordinate is not a factor of second cordinate

<em><u>For (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30</u></em>

Thus first coordinate 6 is factor of second cordinate

<em><u>For (1, 5) , the factors of 5 are 1 and 5</u></em>

Thus first coordinate 1 is a factor of second cordinate

<em><u>For (6, 18) , the factors of 18 are 1, 2, 3, 6, 9, 18</u></em>

Thus first coordinate 6 is factor of second cordinate

<em><u>For (0, 3) , the factors of 3 are 1 and 3</u></em>

Thus first coordinate is not a factor of second cordinate

Summarizing the results:

The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)

<h3>c. Write the ordered pair(s) whose second coordinate is a prime number.</h3>

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Therefore,

(2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

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