If `S= 1821 xx 1923 xx 1827 and T=12` then what is the remainder when S is divided by T?

Options

A. 18
B. 15
C. 12
D. 9

Answer

To find the remainder when \( S = 1821 \times 1923 \times 1827 \) is divided by \( T = 12 \), we can follow these steps:

### Step 1: Find the remainder of each number when divided by 12.

1. **Calculate \( 1821 \mod 12 \)**:
\[ 1821 \div 12 = 151 \quad \text{(quotient)} \]
\[ 1821 - (151 \times 12) = 1821 - 1812 = 9 \quad \text{(remainder)} \]
So, \( 1821 \mod 12 = 9 \).

2. **Calculate \( 1923 \mod 12 \)**:
\[ 1923 \div 12 = 160 \quad \text{(quotient)} \]
\[ 1923 - (160 \times 12) = 1923 - 1920 = 3 \quad \text{(remainder)} \]
So, \( 1923 \mod 12 = 3 \).

3. **Calculate \( 1827 \mod 12 \)**:
\[ 1827 \div 12 = 152 \quad \text{(quotient)} \]
\[ 1827 - (152 \times 12) = 1827 - 1824 = 3 \quad \text{(remainder)} \]
So, \( 1827 \mod 12 = 3 \).

### Step 2: Multiply the remainders obtained.

Now, we multiply the remainders:
\[ 9 \times 3 \times 3 = 81 \]

### Step 3: Find the remainder of the product when divided by 12.

Finally, we need to find \( 81 \mod 12 \):
\[ 81 \div 12 = 6 \quad \text{(quotient)} \]
\[ 81 - (6 \times 12) = 81 - 72 = 9 \quad \text{(remainder)} \]
So, \( 81 \mod 12 = 9 \).

### Conclusion:

The remainder when \( S \) is divided by \( T \) is \( \boxed{9} \).

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