Let's solve the problem step-by-step:
1. First, consider the number [tex]\( n \)[/tex]. According to the problem, when [tex]\( n \)[/tex] is divided by 558, it leaves a remainder of 42. This means we can write:
[tex]\[
n = 558k + 42
\][/tex]
for some integer [tex]\( k \)[/tex].
2. We need to find the remainder when this number [tex]\( n \)[/tex] is divided by 18.
3. Substitute the expression for [tex]\( n \)[/tex] into the division by 18:
[tex]\[
n = 558k + 42
\][/tex]
Find the remainder when [tex]\( 558k + 42 \)[/tex] is divided by 18. We can do this in parts.
4. First, find the remainder when [tex]\( 558k \)[/tex] is divided by 18. Since 558 is a multiple of 18:
[tex]\[
558 = 18 \times 31
\][/tex]
This means that [tex]\( 558k \)[/tex] divided by 18 will leave no remainder, because it is already completely divisible by 18.
5. Next, consider the term 42. Find the remainder when 42 is divided by 18:
[tex]\[
42 \div 18 = 2 \text{ R } 6
\][/tex]
Here, dividing 42 by 18 gives a quotient of 2 and a remainder of 6.
6. Therefore, the remainder when [tex]\( 558k + 42 \)[/tex] is divided by 18 is the same as the remainder when 42 is divided by 18, which is:
[tex]\[
6
\][/tex]
So, the remainder when the number is divided by 18 is [tex]\( 6 \)[/tex].
The correct answer is [tex]\(\boxed{6}\)[/tex].
