Question

review
find the gcf of the following terms. show your work.

1. 9 and 6
2. 15 and 25
3. 12 and 8

variables
find the gcf of the following terms. show your work.

1. x and x²
2. x³ and x⁵
3. y¹⁰ and y²
4. x²y and x²y³
5. xy³ and x⁵y²
6. x³yz and xy²

Explanation:

Step1: List factors of 9, 6

Factors of 9: $1, 3, 9$; Factors of 6: $1, 2, 3, 6$

Step2: Identify common greatest factor

GCF(9,6) = $3$

Step1: List factors of 15, 25

Factors of 15: $1, 3, 5, 15$; Factors of 25: $1, 5, 25$

Step2: Identify common greatest factor

GCF(15,25) = $5$

Step1: List factors of 12, 8

Factors of 12: $1, 2, 3, 4, 6, 12$; Factors of 8: $1, 2, 4, 8$

Step2: Identify common greatest factor

GCF(12,8) = $4$

Step1: Identify lowest exponent of $x$

$x = x^1$, $x^2$; lowest exponent is $1$

Step2: Write GCF with lowest exponent

GCF($x, x^2$) = $x^1 = x$

Step1: Identify lowest exponent of $x$

$x^3$, $x^5$; lowest exponent is $3$

Step2: Write GCF with lowest exponent

GCF($x^3, x^5$) = $x^3$

Step1: Identify lowest exponent of $y$

$y^{10}$, $y^2$; lowest exponent is $2$

Step2: Write GCF with lowest exponent

GCF($y^{10}, y^2$) = $y^2$

Step1: Find GCF for each variable

For $x$: $x^2$ (same exponent); For $y$: $y^1, y^3$, lowest exponent $1$

Step2: Multiply GCF of each variable

GCF($x^2y, x^2y^3$) = $x^2y$

Step1: Find GCF for each variable

For $x$: $x^1, x^5$, lowest exponent $1$; For $y$: $y^3, y^2$, lowest exponent $2$

Step2: Multiply GCF of each variable

GCF($xy^3, x^5y^2$) = $xy^2$

Step1: Find GCF for each variable

For $x$: $x^3, x^1$, lowest exponent $1$; For $y$: $y^1, y^2$, lowest exponent $1$; $z$ only in first term, excluded

Step2: Multiply GCF of each variable

GCF($x^3yz, xy^2$) = $xy$

Answer:

1. $3$
2. $5$
3. $4$
4. $x$
5. $x^3$
6. $y^2$
7. $x^2y$
8. $xy^2$
9. $xy$