What is the highest common factor of \(12x^3\) and \(18x^2\)?

What is the highest common factor of \(12x^3\) and \(18x^2\)?

• A. 6x
• B. 6x^2
• C. 3x^2
• D. 12x^3

Answer: (B)

To determine the highest common factor (HCF) of \(12x^3\) and \(18x^2\), we begin by breaking down each coefficient and variable into their respective factors. The coefficient of \(12x^3\) is 12, which can be factored into \(2^2 \cdot 3\). The coefficient of \(18x^2\) is 18, which can be factored into \(2 \cdot 3^2\). Next, we identify the greatest common factor of the coefficients. For the factors: - From \(12\) (which is \(2^2 \cdot 3\)), we have: - \(2^0\) (not present) or \(2^1\) (the minimum power) contributes \(2^1\). - \(3^1\) (taking the minimum power of \(3\)) contributes \(3^1\). Combining these gives the HCF of the coefficients: \(2^1 \cdot 3^1 = 2 \cdot 3 = 6\). Now, looking at the variable parts, we take the lowest power of \(x

To determine the highest common factor (HCF) of (12x^3) and (18x^2), we begin by breaking down each coefficient and variable into their respective factors.

The coefficient of (12x^3) is 12, which can be factored into (2^2 \cdot 3). The coefficient of (18x^2) is 18, which can be factored into (2 \cdot 3^2).

Next, we identify the greatest common factor of the coefficients. For the factors:

• From (12) (which is (2^2 \cdot 3)), we have:

• (2^0) (not present) or (2^1) (the minimum power) contributes (2^1).

• (3^1) (taking the minimum power of (3)) contributes (3^1).

Combining these gives the HCF of the coefficients: (2^1 \cdot 3^1 = 2 \cdot 3 = 6).

Now, looking at the variable parts, we take the lowest power of (x