Problem Set

1. 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) }

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

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

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

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

Solution:

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) }

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

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

GCF of 15 and 3:

The factors of 3 are: 1, 3

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

Then the greatest common factor is 3

GCF of 6 and 15:

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

GCF of 0 and 3:

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

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

So let us find the factors of second cordinate and check

For (4, 20), the factors of 20 are 1, 2, 4, 5, 10, 20

Thus first coordinate 4 is factor of second cordinate

For (8, 4) the factors of 4 are 1, 2, 4

Thus first coordinate is not a factor of second cordinate

For (2, 3), the factors of 3 are 1, 3

Thus first coordinate is not a factor of second cordinate

For (15, 3), the factors of 3 are 1 and 3

Thus first coordinate is not a factor of second cordinate

For (6, 15), the factors of 15 are 1, 3, 5, 15

Thus first coordinate is not a factor of second cordinate

For (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Thus first coordinate 6 is factor of second cordinate

For (1, 5), the factors of 5 are 1 and 5

Thus first coordinate 1 is a factor of second cordinate

For (6, 18), the factors of 18 are 1, 2, 3, 6, 9, 18

Thus first coordinate 6 is factor of second cordinate

For (0, 3), the factors of 3 are 1 and 3

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)

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

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