Answer:
The greatest common factor of 5x²y⁴ and 12x³y³ is 2xy³.
Explanation:
To find the greatest common factor (GCF) of 5x²y⁴ and 12x³y³, we'll break down each term into its prime factors and then identify the common factors.
Prime factorization of 5x²y⁴:
5 is a prime number.
x² = x * x
y⁴ = y * y * y * y
So, 5x²y⁴ can be expressed as 5 * x * x * y * y * y * y.
Prime factorization of 12x³y³:
12 = 2 * 2 * 3
x³ = x * x * x
y³ = y * y * y
So, 12x³y³ can be expressed as 2 * 2 * 3 * x * x * x * y * y * y.
Now, let's identify the common factors:
Both expressions have a factor of 2.
Both expressions have a factor of x (x to the power of 1 in the first expression and x to the power of 3 in the second expression).
Both expressions have a factor of y (y to the power of 4 in the first expression and y to the power of 3 in the second expression).
To find the GCF, take the lowest power of each common factor:
GCF = 2 * x * y³
So, the greatest common factor of 5x²y⁴ and 12x³y³ is 2xy³.