Finding the HCF of 399 and 437 Using the Division Method
To calculate the Highest Common Factor (HCF) of 399 and 437 using the division method, follow these systematic steps:
Step 1: Initial Division
Start by dividing the larger number (437) by the smaller number (399).
437 ÷ 399 = 1 with a remainder of 38.
So, we can write it as:
437 = 399 × 1 + 38
Step 2: Now, Replace and Repeat
Next, take the previous divisor (399) and divide it by the remainder (38).
399 ÷ 38 = 10 with a remainder of 19.
This can be expressed as:
399 = 38 × 10 + 19
Step 3: Continuing the Process
Now, proceed by dividing the last divisor (38) by the new remainder (19).
38 ÷ 19 = 2 with a remainder of 0.
Expressed mathematically, this looks like:
38 = 19 × 2 + 0
Step 4: Identifying the HCF
Once the remainder is 0, the last non-zero remainder is the HCF. In this case, the last non-zero remainder is 19.
Conclusion
Therefore, the HCF of 399 and 437 is 19.
This division method is an efficient way to determine HCF, ensuring that we systematically eliminate factors until reaching the greatest common divisor.