When `( 43 xx 83)` is divided by 21, the remainder obtained is ?

Options

A. a) 1
B. b) 4
C. c) 20
D. d) 17

Answer

To find the remainder when \( 43 \times 83 \) is divided by 21, we can follow these steps:

### Step 1: Calculate \( 43 \times 83 \)
First, we need to multiply 43 and 83.

\[ 43 \times 83 = 3569 \]

### Step 2: Divide by 21
Next, we will divide 3569 by 21 to find the remainder.

\[ 3569 \div 21 \]

Performing the division, we find:

\[ 3569 \div 21 \approx 169.90476 \]

### Step 3: Calculate the Integer Part
The integer part of the division is 169. Now, we multiply this integer by 21 to find the largest multiple of 21 that is less than or equal to 3569.

\[ 169 \times 21 = 3549 \]

### Step 4: Find the Remainder
Now, we subtract this product from 3569 to find the remainder.

\[ 3569 - 3549 = 20 \]

### Conclusion
Thus, the remainder when \( 43 \times 83 \) is divided by 21 is:

\[ \text{Remainder} = 20 \]