How to Find HCF of two Numbers using Long Division Method?

To find the Highest Common Factor (HCF) of two numbers using the long division method, repeatedly divide the larger number by the smaller number and replace the larger number with the smaller number until the remainder is zero, and the divisor at that step is the HCF.

Follow these steps to find the HCF of two numbers:

Step 1: Divide the larger number by the smaller number, noting the quotient and remainder.

Step 2: Replace the larger number with the smaller number and the smaller number with the remainder obtained.

Step 3: Repeat the process, dividing the new larger number by the new smaller number.

Step 4: Continue until the remainder becomes zero.

Step 5: The divisor at this point is the HCF of the two numbers.

For example:

finding the HCF of 48 and 18 involves steps such as 48 ÷ 18 = 2 with a remainder of 12, then 18 ÷ 12 = 1 with a remainder of 6, and finally 12 ÷ 6 = 2 with a remainder of 0.

At this stage, the divisor (6) is identified as the HCF of 48 and 18.