HCF of 1007 and 1273 is :

Options

A. 1
B. 17
C. 23
D. 19

Answer

To find the Highest Common Factor (HCF) of 1007 and 1273 using the division method, we will follow these steps:

### Step 1: Identify the larger and smaller numbers
- Here, the larger number is 1273 and the smaller number is 1007.

### Step 2: Divide the larger number by the smaller number
- We will divide 1273 by 1007.

\[ 1273 \div 1007 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 1273 - (1 \times 1007) = 1273 - 1007 = 266 \]

### Step 3: Replace the larger number with the smaller number and the smaller number with the remainder
- Now we will replace 1273 with 1007 and 1007 with 266.

### Step 4: Repeat the division
- Now we divide 1007 by 266.

\[ 1007 \div 266 = 3 \quad \text{(quotient)} \]
\[ \text{Remainder} = 1007 - (3 \times 266) = 1007 - 798 = 209 \]

### Step 5: Continue the process
- Next, we divide 266 by 209.

\[ 266 \div 209 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 266 - (1 \times 209) = 266 - 209 = 57 \]

### Step 6: Repeat again
- Now we divide 209 by 57.

\[ 209 \div 57 = 3 \quad \text{(quotient)} \]
\[ \text{Remainder} = 209 - (3 \times 57) = 209 - 171 = 38 \]

### Step 7: Continue dividing
- Next, we divide 57 by 38.

\[ 57 \div 38 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 57 - (1 \times 38) = 57 - 38 = 19 \]

### Step 8: Final division
- Now we divide 38 by 19.

\[ 38 \div 19 = 2 \quad \text{(quotient)} \]
\[ \text{Remainder} = 38 - (2 \times 19) = 38 - 38 = 0 \]

### Step 9: Conclusion
- Since the remainder is now 0, the last non-zero remainder is the HCF. Therefore, the HCF of 1007 and 1273 is 19.

### Final Answer:
- HCF(1007, 1273) = 19

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