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
