Answer:
The greatest common factor (gcf) of [tex]4x^{4}y^{3}[/tex] and [tex]24x^{3}y^{2}[/tex] is 4 x³ y²
Step-by-step explanation:
The greatest common factor of algebraic terms is:
- The greatest common factor of the numbers
- Least exponent of the same variables
Ex: The greatest common factor of 8 x² and 12 x³ is 4 x² because:
The factors of 8 are 1, 2, 4, 8 and the factors of 12 are 1, 2, 3, 4, 6, 12
The common factor of them are 1, 2, 4 and the greatest on is 4
The greatest common factor of x² and x³ is x²
So the gcf of 8 x² and 12 x³ is 4 x²
∵ The terms are [tex]4x^{4}y^{3}[/tex] and [tex]24x^{3}y^{2}[/tex]
∵ The factors of 4 are 1, 2, 4
∵ The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
∴ The common factors of them are 1, 2, 4
∵ The greatest one is 4
∴ The greatest common factor of 4 and 24 is 4
∵ The greatest factor of [tex]x^{4}[/tex] and x³ is x³
∵ The greatest factor of y³ and y² is y²
∴ The greatest common factor of [tex]4x^{4}y^{3}[/tex] and [tex]24x^{3}y^{2}[/tex] is 4 x³ y²
