When `127 xx 139 xx 12653 xx 79 xx 18769` is divided by 5, the remainder obrained is ?

Options

A. 1
B. 2
C. 0
D. 4

Answer

To find the remainder when the expression \(127 \times 139 \times 12653 \times 79 \times 18769\) is divided by 5, we can follow these steps:

### Step 1: Identify the unit digits
To find the remainder when a number is divided by 5, we only need to consider the unit digit of each number in the expression.

- The unit digit of \(127\) is \(7\).
- The unit digit of \(139\) is \(9\).
- The unit digit of \(12653\) is \(3\).
- The unit digit of \(79\) is \(9\).
- The unit digit of \(18769\) is \(9\).

### Step 2: Calculate the remainders of the unit digits when divided by 5
Now, we will find the remainder of each unit digit when divided by 5:

- \(7 \mod 5 = 2\)
- \(9 \mod 5 = 4\)
- \(3 \mod 5 = 3\)
- \(9 \mod 5 = 4\)
- \(9 \mod 5 = 4\)

### Step 3: Multiply the remainders
Next, we will multiply these remainders together:

\[ 2 \times 4 \times 3 \times 4 \times 4 \]

### Step 4: Calculate step by step
1. Calculate \(2 \times 4 = 8\).
2. Now, \(8 \times 3 = 24\).
3. Next, \(24 \times 4 = 96\).
4. Finally, \(96 \times 4 = 384\).

### Step 5: Find the remainder of the product when divided by 5
Now we need to find the remainder of \(384\) when divided by \(5\):

\[ 384 \mod 5 = 4 \]

### Conclusion
The remainder when \(127 \times 139 \times 12653 \times 79 \times 18769\) is divided by \(5\) is \(4\).

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