A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31

Options

A. 3
B. 4
C. 5
D. 6

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step-by-Step Solution:

1. **Identify the number**:
We know that when a number \( x \) is divided by 44, it gives a quotient of 432 and a remainder of 0. This means that the number can be expressed as:
\[ x = 44 \times 432 + 0 \]
Since the remainder is 0, we can simplify this to:
\[ x = 44 \times 432 \]

2. **Calculate the number**:
Now, we will calculate \( x \):
\[ x = 44 \times 432 \]
Performing the multiplication:
\[ x = 19008 \]

3. **Divide the number by 31**:
Next, we need to find the remainder when \( x \) (which is 19008) is divided by 31. We perform the division:
\[ 19008 \div 31 \]

4. **Perform the division**:
Let's calculate it step by step:
- First, determine how many times 31 fits into 19008.
- 31 goes into 19008 approximately 613 times (since \( 31 \times 613 = 19003 \)).
- Now we calculate the product:
\[ 31 \times 613 = 19003 \]

5. **Calculate the remainder**:
Now, we subtract this product from 19008 to find the remainder:
\[ 19008 - 19003 = 5 \]

### Final Answer:
The remainder when 19008 is divided by 31 is **5**.