Which smallest number must be added to 300, so that the resulting number is completely divisible by13?

Options

A. 1
B. 12
C. 10
D. 9

Answer

To solve the problem of finding the smallest number that must be added to 300 so that the resulting number is completely divisible by 13, we can follow these steps:

### Step-by-Step Solution:

1. **Divide 300 by 13**:
We start by dividing 300 by 13 to find out how many times 13 fits into 300 and what the remainder is.
\[ 300 \div 13 = 23 \quad \text{(quotient)} \]
\[ 23 \times 13 = 299 \quad \text{(product)} \]
\[ 300 - 299 = 1 \quad \text{(remainder)} \]

2. **Identify the Remainder**:
From the division, we find that the remainder is 1. This means when 300 is divided by 13, it leaves a remainder of 1.

3. **Calculate the Amount to Add**:
To make 300 completely divisible by 13, we need to eliminate the remainder. We can do this by adding enough to reach the next multiple of 13.
\[ 13 - \text{remainder} = 13 - 1 = 12 \]

4. **Conclusion**:
Therefore, the smallest number that must be added to 300 to make it divisible by 13 is 12.

### Final Answer:
The smallest number that must be added to 300 is **12**.