To determine the greatest common factor (GCF) of the expressions [tex]\(4k\)[/tex], [tex]\(18k^4\)[/tex], and 12, we need to first consider the numerical coefficients and then the algebraic parts (if any).
### Step-by-Step Solution:
1. Identify the Numerical Coefficients:
- For [tex]\(4k\)[/tex], the coefficient is 4.
- For [tex]\(18k^4\)[/tex], the coefficient is 18.
- For 12, the coefficient is 12.
2. Find the GCF of the Numerical Coefficients:
- The common factors of 4 are: 1, 2, 4.
- The common factors of 18 are: 1, 2, 3, 6, 9, 18.
- The common factors of 12 are: 1, 2, 3, 4, 6, 12.
The greatest common factor among 4, 18, and 12 is 2.
3. Consider the Variables:
- The variable part of [tex]\(4k\)[/tex] is [tex]\(k\)[/tex].
- The variable part of [tex]\(18k^4\)[/tex] is [tex]\(k^4\)[/tex].
- There is no variable part in 12.
Since one of the terms (12) does not contain the variable [tex]\(k\)[/tex], we do not include any variable in the GCF.
### Conclusion:
The greatest common factor of [tex]\(4k\)[/tex], [tex]\(18k^4\)[/tex], and 12 is 2.
So, the correct answer to the question is:
[tex]\[ \boxed{2} \][/tex]
