Question: Find the greatest common factor of these two expressions. $$8u^3y^7 \quad \text{and} \quad…

Find the greatest common factor of these two expressions.

$$8u^3y^7 \quad \text{and} \quad 20u^4y^2w$$

Solution

To find the greatest common factor (GCF) of the expressions \(8u^3y^7\) and \(20u^4y^2w\), follow these steps: Identify the GCF of the coefficients: - The coefficients are 8 and 20. - The GCF of 8 and 20 is 4. Identify the GCF of the variables by comparing the powers: For \(u\): - The powers are 3 and 4. - The GCF is the lower power, which is \(u^3\). For \(y\): - The powers are 7 and 2. - The GCF is the lower power, which is \(y^2\). For \(w\): - The first expression has no \(w\), so the GCF is \(w^0 = 1\). Combine these GCFs: \[ 4u^3y^2 \] Therefore, the greatest common factor of \(8u^3y^7\) and \(20u^4y^2w\) is \(4u^3y^2\).