Choose the set of numbers from the four alternative sets, which is similar to the given set.
Given set : (2, 14, 16)

Options

A. (2,7,8)
B. (2, 9, 16)
C. (3, 21, 24)
D. (4, 16, 18)

Explanation

To solve the problem, we need to identify a set of numbers that is similar to the given set (2, 14, 16). We can do this by finding a common factor among the numbers in the given set and then looking for an alternative set that follows the same pattern.

### Step-by-Step Solution:

1. **Identify the Given Set**:
The given set is (2, 14, 16).

2. **Find the Common Factor**:
We can see that 2 is a common factor of the numbers in the given set.
- 2 can be factored out as follows:
- 2 = 2 * 1
- 14 = 2 * 7
- 16 = 2 * 8

3. **Express the Given Set in Terms of the Common Factor**:
We can express the given set as:
- (2 * 1, 2 * 7, 2 * 8) or (2, 7 * 2, 8 * 2)

4. **Look for Alternative Sets**:
We need to check the four alternative sets provided (not specified in the question) to see which one can be expressed in a similar way using a common factor.

5. **Evaluate Each Alternative Set**:
- For each alternative set, check if there is a common factor that can be factored out in a similar way.
- For example, if we have an alternative set (3, 21, 24):
- 3 = 3 * 1
- 21 = 3 * 7
- 24 = 3 * 8
- This can be expressed as (3 * 1, 3 * 7, 3 * 8), which is similar to the given set.

6. **Select the Correct Alternative Set**:
After evaluating the alternative sets, we find that the set (3, 21, 24) follows the same pattern as the given set (2, 14, 16) because both can be expressed using a common factor.

### Conclusion:
The alternative set that is similar to the given set (2, 14, 16) is (3, 21, 24).

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