What will be the remainder when (`631 xx 632 xx 633`) is divided by 5?

Options

A. 6
B. 1
C. 4
D. 3

Answer

To find the remainder when \( 631 \times 632 \times 633 \) is divided by 5, we can follow these steps:

### Step 1: Find the remainders of each number when divided by 5
- For \( 631 \):
\[ 631 \div 5 = 126 \quad \text{(remainder: 1)} \]
So, \( 631 \equiv 1 \mod 5 \).

- For \( 632 \):
\[ 632 \div 5 = 126 \quad \text{(remainder: 2)} \]
So, \( 632 \equiv 2 \mod 5 \).

- For \( 633 \):
\[ 633 \div 5 = 126 \quad \text{(remainder: 3)} \]
So, \( 633 \equiv 3 \mod 5 \).

### Step 2: Multiply the remainders
Now, we multiply the remainders we found:
\[ 1 \times 2 \times 3 = 6 \]

### Step 3: Find the remainder of the product when divided by 5
Next, we find the remainder of 6 when divided by 5:
\[ 6 \div 5 = 1 \quad \text{(remainder: 1)} \]

### Conclusion
Thus, the remainder when \( 631 \times 632 \times 633 \) is divided by 5 is:
\[ \boxed{1} \]