Multiply `2056` by `87`.

Options

A. `178872`
B. `181772`
C. `205600`
D. None of these

Answer

To solve the multiplication of `2056` by `87`, we can break it down into simpler steps:

### Step 1: Break down the multiplication
We can express `87` as `80 + 7`. This allows us to multiply `2056` by `80` and `7` separately.

### Step 2: Multiply `2056` by `7`
Now, we will calculate:
\[ 2056 \times 7 \]

1. **Multiply the units place:**
\( 6 \times 7 = 42 \)
Write down `2` and carry over `4`.

2. **Multiply the tens place:**
\( 5 \times 7 = 35 \)
Add the carry: \( 35 + 4 = 39 \)
Write down `9` and carry over `3`.

3. **Multiply the hundreds place:**
\( 0 \times 7 = 0 \)
Add the carry: \( 0 + 3 = 3 \)
Write down `3`.

4. **Multiply the thousands place:**
\( 2 \times 7 = 14 \)
Write down `14`.

So, \( 2056 \times 7 = 14392 \).

### Step 3: Multiply `2056` by `80`
Next, we calculate:
\[ 2056 \times 80 \]
Since \( 80 = 8 \times 10 \), we can first multiply by `8` and then add a zero at the end.

1. **Multiply `2056` by `8`:**
- **Multiply the units place:**
\( 6 \times 8 = 48 \)
Write down `8` and carry over `4`.

- **Multiply the tens place:**
\( 5 \times 8 = 40 \)
Add the carry: \( 40 + 4 = 44 \)
Write down `4` and carry over `4`.

- **Multiply the hundreds place:**
\( 0 \times 8 = 0 \)
Add the carry: \( 0 + 4 = 4 \)
Write down `4`.

- **Multiply the thousands place:**
\( 2 \times 8 = 16 \)
Write down `16`.

So, \( 2056 \times 8 = 16448 \).

2. **Now, add a zero for the tens place:**
\( 16448 \) becomes \( 164480 \).

### Step 4: Add the two results
Now we will add the results of the two multiplications:
\[ 14392 + 164480 \]

Aligning the numbers for addition:
```
164480
+ 14392
__________
```

1. **Add the units place:**
\( 0 + 2 = 2 \)

2. **Add the tens place:**
\( 8 + 9 = 17 \)
Write down `7` and carry over `1`.

3. **Add the hundreds place:**
\( 4 + 3 = 7 \)
Add the carry: \( 7 + 1 = 8 \).

4. **Add the thousands place:**
\( 4 + 4 = 8 \).

5. **Add the ten-thousands place:**
\( 1 + 0 = 1 \).

So, the final result is:
\[ 2056 \times 87 = 178872 \]

### Final Answer
The product of `2056` and `87` is `178872`.

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