If a number divides sum of two numbers, then it divides the two numbers separately also.

Answer

To prove the statement "If a number divides the sum of two numbers, then it divides the two numbers separately also," we can follow these steps:

### Step-by-Step Solution:

1. **Define the Numbers**: Let \( a \) and \( b \) be two numbers, and let \( c \) be a number that divides the sum of \( a \) and \( b \).

2. **Express the Condition**: According to the problem, we have:
\[ c \text{ divides } (a + b) \]
This means that there exists an integer \( k \) such that:
\[ a + b = c \cdot k \]

3. **Use the Division Property**: We need to show that \( c \) divides \( a \) and \( c \) divides \( b \). To do this, we can express \( a \) and \( b \) in terms of \( c \):
\[ a = c \cdot m \quad \text{(for some integer } m\text{)} \]
\[ b = c \cdot n \quad \text{(for some integer } n\text{)} \]

4. **Substitute into the Sum**: Now substitute \( a \) and \( b \) back into the equation for \( a + b \):
\[ a + b = (c \cdot m) + (c \cdot n) = c \cdot (m + n) \]

5. **Conclusion**: Since \( a + b = c \cdot (m + n) \), it shows that \( c \) divides \( a + b \). Therefore, if \( c \) divides the sum \( a + b \), it must also divide both \( a \) and \( b \) separately.

### Final Statement:
Thus, we have proved that if a number \( c \) divides the sum of two numbers \( a \) and \( b \), then \( c \) divides both \( a \) and \( b \) separately.

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