In finding the HCF of two numbers by division method, the last divisor is 174 and the quotient are 1, 7 and 2, respectively. If the sum of the two numbers is divided by 11. the remainder is:

Options

A. 2
B. 8
C. 1
D. 7

Answer

To find the remainder when the sum of two numbers is divided by 11, we can follow these steps:

### Step 1: Identify the last divisor and the quotients
The last divisor is given as 174. The quotients are 1, 7, and 2.

### Step 2: Calculate the second last dividend
Using the last divisor and the last quotient:
- Second last dividend = Last divisor × Last quotient
- Second last dividend = 174 × 2 = 348

### Step 3: Calculate the first dividend
Now, using the second last dividend and the second last quotient:
- First dividend = Second last dividend × Second last quotient + Last divisor
- First dividend = 348 × 7 + 174
- First dividend = 2436 + 174 = 2610

### Step 4: Calculate the first number
Now, we have the first dividend as 2610.

### Step 5: Calculate the sum of the two numbers
Now, we can find the sum of the two numbers:
- Sum of the two numbers = First dividend + Second last dividend
- Sum of the two numbers = 2610 + 348 = 2958

### Step 6: Calculate the sum of the two numbers
Now, we can find the sum of the two numbers:
- Sum of the two numbers = 2610 + 2958 = 5568

### Step 7: Find the remainder when the sum is divided by 11
Now, we need to divide the sum (5568) by 11 and find the remainder:
- 5568 ÷ 11 = 506 remainder 2

### Conclusion
The remainder when the sum of the two numbers is divided by 11 is **2**.

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