**Finding the HCF using Short Division Method**

The Highest Common Factor (HCF) is the largest number that divides two or more given numbers without leaving any remainder. One of the methods to find the HCF is the short division method. In this method, we divide the given numbers by the smallest prime numbers and keep dividing until we cannot divide anymore. Let's understand the steps involved in finding the HCF using the short division method.

**Step 1: Identify the given numbers**
- Let's say we have two numbers, A and B, for which we need to find the HCF.

**Step 2: Find the smallest prime number**
- Start by finding the smallest prime number that can divide both A and B. The smallest prime number is 2.

**Step 3: Divide the numbers by the smallest prime number**
- Divide both A and B by 2. If the numbers are divisible by 2, keep dividing until they are no longer divisible.

**Step 4: Write the quotient and remainder**
- Write down the quotient and remainder after each division.

**Step 5: Continue dividing by the next prime numbers**
- Repeat steps 3 and 4 with the next prime numbers (3, 5, 7, 11, and so on) until we cannot divide any further.

**Step 6: Identify the common prime factors**
- Identify the common prime factors obtained from the divisions.

**Step 7: Multiply the common prime factors**
- Multiply all the common prime factors obtained in step 6 to find the HCF of the given numbers.

**Step 8: Simplify the HCF**
- If the HCF contains any common factors, simplify it to the simplest form.

By following these steps, we can find the HCF of any given numbers using the short division method. It is a systematic approach that ensures we do not miss any common factors among the given numbers. Practice and familiarity with prime numbers will help in performing the divisions quickly and efficiently.