Let's analyze each option to determine which one is a factor of 24 but not a multiple of 6.
### Step-by-Step Solution:
1. Option a: 8
- Is 8 a factor of 24?
- Yes, because [tex]\(24 \div 8 = 3\)[/tex]. Hence, [tex]\(8 \times 3 = 24\)[/tex].
- Is 8 a multiple of 6?
- No, because [tex]\(8 \div 6\)[/tex] does not yield a whole number.
Since 8 is a factor of 24 but not a multiple of 6, it satisfies the conditions.
2. Option b: 12
- Is 12 a factor of 24?
- Yes, because [tex]\(24 \div 12 = 2\)[/tex]. Hence, [tex]\(12 \times 2 = 24\)[/tex].
- Is 12 a multiple of 6?
- Yes, because [tex]\(12 \div 6 = 2\)[/tex].
Since 12 is a multiple of 6, it does not satisfy the conditions.
3. Option c: 10
- Is 10 a factor of 24?
- No, because [tex]\(24 \div 10\)[/tex] does not yield a whole number.
Since 10 is not a factor of 24, it does not satisfy the conditions.
4. Option d: 7
- Is 7 a factor of 24?
- No, because [tex]\(24 \div 7\)[/tex] does not yield a whole number.
Since 7 is not a factor of 24, it does not satisfy the conditions.
### Conclusion:
After evaluating all options, we find that Option a: 8 is the number that is a factor of 24 but not a multiple of 6.
So, the answer is:
8
