Question

Using prime factorisation, find the HCF of 144, 180 and 192.

Answer 1

Given:
Find HCF of 144, 180, and 192 using prime factorisation.

Step 1: Prime factorisation of each number
\[ 144 = 2^4 \times 3^2 \] \[ 180 = 2^2 \times 3^2 \times 5 \] \[ 192 = 2^6 \times 3 \]

Step 2: Identify common prime factors with smallest powers
- For prime factor 2: smallest power among 4, 2, 6 is \(2\).
- For prime factor 3: smallest power among 2, 2, 1 is \(1\).
- Prime factor 5 is not common to all.

Step 3: Calculate HCF
\[ \text{HCF} = 2^2 \times 3^1 = 4 \times 3 = 12 \]

Final Answer:
\[ \boxed{12} \]