In finding the HCF of two numbers by division method, the last divisor is 49 and the quoticnts are 17,3,2 .Find the two numbers

Options

A. 243 and 4929
B. 343 and 5929
C. 334 and 5992
D. None of these

Answer

To find the two numbers whose HCF is given as 49 and the quotients are 17, 3, and 2, we can follow these steps:

### Step 1: Understand the Division Method
In the division method for finding the HCF, we have a series of divisions where the last divisor is the HCF. The quotients obtained from these divisions help us find the original numbers.

### Step 2: Identify the Last Divisor
The last divisor given is 49. This means that the HCF of the two numbers is 49.

### Step 3: Use the Quotients to Find the First Number
The first quotient is 17. According to the division method, we can express the first number (let's call it \( A \)) as:
\[ A = \text{(Last Divisor)} \times \text{(First Quotient)} + \text{(Remainder)} \]
Since the last divisor is 49 and there is no remainder mentioned, we can assume the remainder is 0. Thus:
\[ A = 49 \times 17 + 0 = 49 \times 17 \]

Calculating \( A \):
\[ A = 49 \times 17 = 833 \]

### Step 4: Use the Second Quotient to Find the Second Number
The second quotient is 3. We can express the second number (let's call it \( B \)) in a similar way:
\[ B = \text{(Last Divisor)} \times \text{(Second Quotient)} + \text{(Remainder)} \]
Again, assuming the remainder is 0:
\[ B = 49 \times 3 + 0 = 49 \times 3 \]

Calculating \( B \):
\[ B = 49 \times 3 = 147 \]

### Step 5: Use the Third Quotient to Find the Third Number
The third quotient is 2. We can express the third number (let's call it \( C \)) as:
\[ C = \text{(Last Divisor)} \times \text{(Third Quotient)} + \text{(Remainder)} \]
Assuming the remainder is 0:
\[ C = 49 \times 2 + 0 = 49 \times 2 \]

Calculating \( C \):
\[ C = 49 \times 2 = 98 \]

### Final Result
Thus, the two numbers are:
1. \( A = 833 \)
2. \( B = 147 \)

### Summary of the Two Numbers
The two numbers are 833 and 147.

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