Sure, let's find the Greatest Common Factor (GCF) of each pair of monomials step-by-step.
### 1. Finding the GCF of [tex]\(8 x^2 y\)[/tex] and [tex]\(16 x y\)[/tex]:
1. Identify the numerical coefficients: - The numerical coefficients are [tex]\(8\)[/tex] and [tex]\(16\)[/tex].
2. Find the GCF of the numerical coefficients: - The GCF of [tex]\(8\)[/tex] and [tex]\(16\)[/tex] is [tex]\(8\)[/tex].
3. Identify the variable parts with their exponents: - For [tex]\(8 x^2 y\)[/tex], we have [tex]\(x^2\)[/tex] and [tex]\(y^1\)[/tex]. - For [tex]\(16 x y\)[/tex], we have [tex]\(x^1\)[/tex] and [tex]\(y^1\)[/tex].
4. Find the GCF of the variable parts: - For [tex]\(x\)[/tex]: The minimum exponent is [tex]\(1\)[/tex], so [tex]\(x^1 = x\)[/tex]. - For [tex]\(y\)[/tex]: The minimum exponent is [tex]\(1\)[/tex], so [tex]\(y^1 = y\)[/tex].
Combining the GCF of the numerical coefficients and the variable parts, the GCF of [tex]\(8 x^2 y\)[/tex] and [tex]\(16 x y\)[/tex] is: [tex]\[8xy\][/tex]
### 2. Finding the GCF of [tex]\(8 a b^3\)[/tex] and [tex]\(10 a^2 b^2\)[/tex]:
1. Identify the numerical coefficients: - The numerical coefficients are [tex]\(8\)[/tex] and [tex]\(10\)[/tex].
2. Find the GCF of the numerical coefficients: - The GCF of [tex]\(8\)[/tex] and [tex]\(10\)[/tex] is [tex]\(2\)[/tex].
3. Identify the variable parts with their exponents: - For [tex]\(8 a b^3\)[/tex], we have [tex]\(a^1\)[/tex] and [tex]\(b^3\)[/tex]. - For [tex]\(10 a^2 b^2\)[/tex], we have [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex].
4. Find the GCF of the variable parts: - For [tex]\(a\)[/tex]: The minimum exponent is [tex]\(1\)[/tex], so [tex]\(a^1 = a\)[/tex]. - For [tex]\(b\)[/tex]: The minimum exponent is [tex]\(2\)[/tex], so [tex]\(b^2 = b^2\)[/tex].
Combining the GCF of the numerical coefficients and the variable parts, the GCF of [tex]\(8 a b^3\)[/tex] and [tex]\(10 a^2 b^2\)[/tex] is: [tex]\[2ab^2\][/tex]
So, the GCFs are: 1. [tex]\(8xy\)[/tex] 2. [tex]\(2ab^2\)[/tex]
