To find the greatest common factor (GCF) of the terms [tex]\( 24 s^3 \)[/tex], [tex]\( 12 s^4 \)[/tex], and [tex]\( 18 s \)[/tex], we need to consider both the coefficients and the variable parts separately.
### Step-by-Step Solution:
1. Identify the coefficients and the powers of [tex]\( s \)[/tex]:
- For [tex]\( 24 s^3 \)[/tex], the coefficient is 24 and the power of [tex]\( s \)[/tex] is 3.
- For [tex]\( 12 s^4 \)[/tex], the coefficient is 12 and the power of [tex]\( s \)[/tex] is 4.
- For [tex]\( 18 s \)[/tex], the coefficient is 18 and the power of [tex]\( s \)[/tex] is 1.
2. Find the greatest common divisor (GCD) of the coefficients:
- The coefficients are 24, 12, and 18.
- To find the GCD of these three numbers:
[tex]\[
\text{GCD}(24, 12, 18) = 6
\][/tex]
3. Find the smallest power of [tex]\( s \)[/tex]:
- The powers of [tex]\( s \)[/tex] are 3, 4, and 1.
- The smallest power among these is 1.
4. Combine the GCD of the coefficients and the smallest power of [tex]\( s \)[/tex]:
- The GCD of the coefficients is 6.
- The smallest power of [tex]\( s \)[/tex] is [tex]\( s^1 \)[/tex].
Therefore, the greatest common factor of the terms [tex]\( 24 s^3 \)[/tex], [tex]\( 12 s^4 \)[/tex], and [tex]\( 18 s \)[/tex] is:
[tex]\[
6 s^1 \text{ or } 6 s
\][/tex]
### Conclusion:
The greatest common factor of [tex]\( 24 s^3 \)[/tex], [tex]\( 12 s^4 \)[/tex], and [tex]\( 18 s \)[/tex] is [tex]\( 6 s \)[/tex].
