What least number must be subtracted from 3401, so that the sum is completely divisible by 11?

Options

A. 3
B. 1
C. 2
D. 0

Answer

To solve the problem of finding the least number that must be subtracted from 3401 so that the result is completely divisible by 11, we can follow these steps:

### Step 1: Divide 3401 by 11
First, we need to perform the division of 3401 by 11 to find the remainder.

\[ 3401 \div 11 \]

### Step 2: Calculate the quotient and remainder
Let's calculate it step by step:

1. **Divide the first digit**: 3 divided by 11 is 0 (since 3 is less than 11).
2. **Consider the first two digits**: 34 divided by 11 gives 3 (since \(11 \times 3 = 33\)).
3. **Subtract**:
\[ 34 - 33 = 1 \]
4. **Bring down the next digit**: Now we have 10 (from 1 and the next digit 0).
5. **Divide 10 by 11**: 10 divided by 11 is 0.
6. **Bring down the next digit**: Now we have 100.
7. **Divide 100 by 11**: 100 divided by 11 gives 9 (since \(11 \times 9 = 99\)).
8. **Subtract**:
\[ 100 - 99 = 1 \]
9. **Bring down the last digit**: Now we have 11.
10. **Divide 11 by 11**: 11 divided by 11 is 1 (since \(11 \times 1 = 11\)).
11. **Subtract**:
\[ 11 - 11 = 0 \]

Thus, the complete division gives us a quotient of 309 and a remainder of 2.

### Step 3: Determine the least number to subtract
Now, since the remainder is 2, this means that 3401 is 2 more than a multiple of 11. To make 3401 divisible by 11, we need to subtract this remainder from 3401.

\[ \text{Least number to subtract} = 2 \]

### Conclusion
Therefore, the least number that must be subtracted from 3401 so that the result is completely divisible by 11 is:

\[ \boxed{2} \]

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