Given that 6 is a divisor of r and r is a factor of s, is 6 a factor of s?

Answer

To determine whether 6 is a factor of s given that 6 is a divisor of r and r is a factor of s, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the first statement**:
- We know that 6 is a divisor of r. This means that r can be expressed as:
\[ r = 6n \]
where n is some integer.

2. **Understanding the second statement**:
- The second statement tells us that r is a factor of s. This means that s can be expressed as:
\[ s = rm \]
where m is some integer.

3. **Substituting the expression for r into the equation for s**:
- Now, we can substitute the expression for r from the first statement into the second statement:
\[ s = (6n)m \]
- This simplifies to:
\[ s = 6(nm) \]
- Here, (nm) is also an integer since the product of two integers is an integer.

4. **Conclusion**:
- Since s can be expressed as \(s = 6k\) where \(k = nm\) (an integer), we conclude that 6 is indeed a factor of s.

### Final Answer:
Yes, 6 is a factor of s.