Find the HCF of the numbers in each of the following, using the division method :
399, 437

Answer

To find the HCF (Highest Common Factor) of the numbers 399 and 437 using the division method, we can follow these steps:

### Step 1: Identify the larger and smaller number
- Here, we have two numbers: 399 and 437. The larger number is 437 and the smaller number is 399.

### Step 2: Divide the larger number by the smaller number
- We divide 437 by 399.

\[ 437 \div 399 = 1 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 437 - (1 \times 399) = 437 - 399 = 38 \]

### Step 3: Replace the larger number with the smaller number and the smaller number with the remainder
- Now we take the smaller number (399) and the remainder (38) for the next step.

### Step 4: Divide the new pair of numbers
- We divide 399 by 38.

\[ 399 \div 38 = 10 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 399 - (10 \times 38) = 399 - 380 = 19 \]

### Step 5: Repeat the process
- Now we take 38 and 19 for the next step.

### Step 6: Divide again
- We divide 38 by 19.

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

### Step 7: Conclusion
- Since we have reached a remainder of 0, the last non-zero remainder (which is 19) is the HCF of 399 and 437.

Thus, the HCF of 399 and 437 is **19**.

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