Find the Common Factor of 22abc - 11ab/c: Algebraic Expression Analysis

To find the common factor for the expression $22abc - \frac{11ab}{c}$, we will follow these steps:

• Step 1: Determine the common factors in terms of coefficients and variables.
• Step 2: Factor these common elements out of the expression.
• Step 3: Simplify the expression after factoring.

Now, let's proceed with the solution:

Step 1: Identify the common factors.
The expression is $22abc - \frac{11ab}{c}$. We can see that both terms have the factors $11ab$. 11 is a common numerical factor in 22 and 11. Ab is also present in both terms.

Step 2: Factor out the common factors.
Factor out $11ab$ from each term in the expression:

$22abc - \frac{11ab}{c} = 11ab \left( \frac{22abc}{11ab} - \frac{\left(\frac{11ab}{c}\right)}{11ab} \right)$

Step 3: Simplify the terms inside the parenthesis.

• Simplify the first term: $\frac{22abc}{11ab} = 2c$
• Simplify the second term: $\frac{\frac{11ab}{c}}{11ab} = \frac{1}{c}$

Thus, we get the factored form:

$11ab\left(2c - \frac{1}{c}\right)$

Therefore, the common factor form of $22abc - \frac{11ab}{c}$ is $11ab(2c - \frac{1}{c})$.