To factor out the greatest common factor (GCF), we first identify the GCF of the coefficients in the given expression [tex]\(22c + 33d\)[/tex].
Step-by-step solution:
1. Find the GCF of the coefficients:
- The coefficients in the expression are 22 and 33.
- To find the GCF, we look for the largest number that divides both 22 and 33 without any remainder.
- The factors of 22 are: 1, 2, 11, 22.
- The factors of 33 are: 1, 3, 11, 33.
- The common factors of 22 and 33 are: 1, 11.
- Therefore, the greatest common factor is 11.
2. Factor out the GCF from the expression:
- The original expression is [tex]\(22c + 33d\)[/tex].
- We will factor out 11 from both terms.
- Divide each term by the GCF (11):
[tex]\[
\frac{22c}{11} + \frac{33d}{11} = 2c + 3d
\][/tex]
3. Write the expression as a product of the GCF and the resulting expression:
- After factoring out 11, the expression can be written as:
[tex]\[
11 \cdot (2c + 3d)
\][/tex]
Thus, the factored form of the expression [tex]\(22c + 33d\)[/tex] is:
[tex]\[
22c + 33d = 11(2c + 3d)
\][/tex]
