On dividing `111a ^(2) b ^(2) c ^(2) by 37 a ^(2),` we get ____

Options

A. `2c ^(3)`
B. `2b ^(2)`
C. `3`
D. `3b ^(2)c^(2)`

Answer

To solve the problem of dividing \( 111a^2b^2c^2 \) by \( 37a^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Write the Division Expression**:
We start with the expression:
\[ \frac{111a^2b^2c^2}{37a^2} \]

2. **Cancel Common Terms**:
Since both the numerator and the denominator have \( a^2 \), we can cancel \( a^2 \) from both:
\[ = \frac{111b^2c^2}{37} \]

3. **Divide the Coefficients**:
Next, we divide the coefficients \( 111 \) by \( 37 \):
\[ 111 \div 37 = 3 \]
(This is because \( 37 \times 3 = 111 \))

4. **Combine the Remaining Terms**:
After dividing, we are left with:
\[ 3b^2c^2 \]

5. **Final Result**:
Therefore, the final result of the division is:
\[ 3b^2c^2 \]

### Final Answer:
The answer to the question is \( 3b^2c^2 \).

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