Which smallest number must be added to 100, so that the resulting number is completely divisible by 6?

Options

A. 2
B. 3
C. 5
D. 4

Answer

To find the smallest number that must be added to 100 so that the resulting number is completely divisible by 6, we can follow these steps:

### Step 1: Divide 100 by 6
We start by dividing 100 by 6 to find out how much is left over (the remainder).

\[ 100 \div 6 = 16 \quad \text{(whole number part)} \]
\[ 16 \times 6 = 96 \quad \text{(to find the largest multiple of 6 less than 100)} \]

### Step 2: Calculate the remainder
Now we subtract this product from 100 to find the remainder.

\[ 100 - 96 = 4 \]

### Step 3: Determine how much more is needed to reach the next multiple of 6
Since the remainder is 4, we need to find out how much more we need to add to 100 to make it divisible by 6. The next multiple of 6 after 96 is 102.

\[ 102 - 100 = 2 \]

### Conclusion
Therefore, the smallest number that must be added to 100 to make it completely divisible by 6 is:

\[ \boxed{2} \]