**Prime Factorisation Method to Find HCF of 144 and 198**

The prime factorisation method is a systematic approach to find the highest common factor (HCF) of two numbers. In this method, we express both numbers as a product of their prime factors and then identify the common prime factors. The HCF is obtained by multiplying these common prime factors together. Let's find the HCF of 144 and 198 using the prime factorisation method.

**Step 1: Prime Factorisation of 144**

To begin, we need to express the number 144 as a product of its prime factors. We divide 144 by the smallest prime number, which is 2.

144 ÷ 2 = 72

We continue dividing the quotient by 2 until we can no longer divide evenly.

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9

Now, we move on to the next prime number, which is 3.

9 ÷ 3 = 3

Since 3 is a prime number, we stop here. Therefore, the prime factorisation of 144 is 2 × 2 × 2 × 2 × 3 × 3 = 2^4 × 3^2.

**Step 2: Prime Factorisation of 198**

Next, we need to express the number 198 as a product of its prime factors. We divide 198 by the smallest prime number, which is 2.

198 ÷ 2 = 99

We continue dividing the quotient by 3 since 99 is not divisible by 2.

99 ÷ 3 = 33

Now, we move on to the next prime number, which is 3.

33 ÷ 3 = 11

Since 11 is a prime number, we stop here. Therefore, the prime factorisation of 198 is 2 × 3 × 3 × 11 = 2^1 × 3^2 × 11^1.

**Step 3: Identify Common Prime Factors**

To find the HCF, we need to identify the common prime factors of 144 and 198. From their prime factorisations, we can see that both numbers have 2 and 3 as common prime factors.

**Step 4: Multiply Common Prime Factors**

Finally, we multiply the common prime factors together to obtain the HCF.

HCF = 2 × 3 = 6

Therefore, the highest common factor (HCF) of 144 and 198 is 6.