Question

name:

bpa math - greatest common factor (gcf)

12
1 * 12
2 * 6
3 * 4

8
1 * 8
2 * 4

11
1 * 11

30
1 * 30
2 * 15
3 * 10
5 * 6

list all factor pairs for the following numbers:

1. 4

1. 5

1. 6

1. 10

1. 21

1. 18

1. 14

1. 16

1. 36

e1) ( x^3 )
( (1, x^3) ), ( (x, x^2) ), ( (x^2, x) )

e2) ( y^4 )
( (1, y^4) ), ( (y, y^3) ), ( (y^2, y^2) ), ( (y^3, y) ), ( (y^4, 1) )

e3) ( x^2y )

Explanation:

Step1: List factor pairs for 4

Find pairs multiplying to 4:
$1 * 4$, $2 * 2$

Step2: List factor pairs for 5

Find pairs multiplying to 5:
$1 * 5$

Step3: List factor pairs for 6

Find pairs multiplying to 6:
$1 * 6$, $2 * 3$

Step4: List factor pairs for 10

Find pairs multiplying to 10:
$1 * 10$, $2 * 5$

Step5: List factor pairs for 21

Find pairs multiplying to 21:
$1 * 21$, $3 * 7$

Step6: List factor pairs for 18

Find pairs multiplying to 18:
$1 * 18$, $2 * 9$, $3 * 6$

Step7: List factor pairs for 14

Find pairs multiplying to 14:
$1 * 14$, $2 * 7$

Step8: List factor pairs for 16

Find pairs multiplying to 16:
$1 * 16$, $2 * 8$, $4 * 4$

Step9: List factor pairs for 36

Find pairs multiplying to 36:
$1 * 36$, $2 * 18$, $3 * 12$, $4 * 9$, $6 * 6$

Step10: List factor pairs for $x^3$

Find monomial pairs multiplying to $x^3$:
$1 * x^3$, $x * x^2$, $x^2 * x$, $x^3 * 1$

Step11: List factor pairs for $y^4$

Find monomial pairs multiplying to $y^4$:
$1 * y^4$, $y * y^3$, $y^2 * y^2$, $y^3 * y$, $y^4 * 1$

Step12: List factor pairs for $x^2y$

Find monomial pairs multiplying to $x^2y$:
$1 * x^2y$, $x * xy$, $x^2 * y$, $y * x^2$, $xy * x$, $x^2y * 1$

Answer:

1. $1 * 4$, $2 * 2$
2. $1 * 5$
3. $1 * 6$, $2 * 3$
4. $1 * 10$, $2 * 5$
5. $1 * 21$, $3 * 7$
6. $1 * 18$, $2 * 9$, $3 * 6$
7. $1 * 14$, $2 * 7$
8. $1 * 16$, $2 * 8$, $4 * 4$
9. $1 * 36$, $2 * 18$, $3 * 12$, $4 * 9$, $6 * 6$

E1) $1 * x^3$, $x * x^2$, $x^2 * x$, $x^3 * 1$
E2) $1 * y^4$, $y * y^3$, $y^2 * y^2$, $y^3 * y$, $y^4 * 1$
E3) $1 * x^2y$, $x * xy$, $x^2 * y$, $y * x^2$, $xy * x$, $x^2y * 1$