Find the remainder in expression–
`(1372 xx 1276)/(9)`

Options

A. 1
B. 2
C. 3
D. 7

Answer

To find the remainder of the expression \( \frac{1372 \times 1276}{9} \), we can follow these steps:

### Step 1: Find the remainder of 1372 when divided by 9
To find the remainder, we can perform the division:

1. Divide 1372 by 9.
2. Calculate \( 1372 \div 9 \):
- 9 goes into 13 once (1), leaving a remainder of 4 (13 - 9).
- Bring down the next digit (7), making it 47.
- 9 goes into 47 five times (5), leaving a remainder of 2 (47 - 45).
- Bring down the next digit (2), making it 22.
- 9 goes into 22 two times (2), leaving a remainder of 4 (22 - 18).

Thus, the remainder when 1372 is divided by 9 is **4**.

### Step 2: Find the remainder of 1276 when divided by 9
Now, we will find the remainder of 1276:

1. Divide 1276 by 9.
2. Calculate \( 1276 \div 9 \):
- 9 goes into 12 once (1), leaving a remainder of 3 (12 - 9).
- Bring down the next digit (7), making it 37.
- 9 goes into 37 four times (4), leaving a remainder of 1 (37 - 36).
- Bring down the next digit (6), making it 16.
- 9 goes into 16 once (1), leaving a remainder of 7 (16 - 9).

Thus, the remainder when 1276 is divided by 9 is **7**.

### Step 3: Multiply the remainders
Now we multiply the remainders we found in the previous steps:

\[ \text{Remainder of } 1372 \times 1276 \mod 9 = (4 \times 7) \mod 9 \]

Calculating \( 4 \times 7 = 28 \).

### Step 4: Find the remainder of 28 when divided by 9
Now, we need to find the remainder of 28 when divided by 9:

1. Divide 28 by 9.
2. Calculate \( 28 \div 9 \):
- 9 goes into 28 three times (3), leaving a remainder of 1 (28 - 27).

Thus, the remainder when 28 is divided by 9 is **1**.

### Final Answer
Therefore, the remainder of the expression \( \frac{1372 \times 1276}{9} \) is **1**.

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