Question

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

Answer 1

Given:
Calculate the Highest Common Factor (HCF) of 144, 180, and 192 using prime factorization.

Step 1: Prime factorization
\[144 = 2^4 \times 3^2\] \[180 = 2^2 \times 3^2 \times 5\] \[192 = 2^6 \times 3\]

Step 2: Identify common prime factors and their lowest powers
- Prime factor 2: The smallest power is \(2\) (from \(2^4\), \(2^2\), and \(2^6\)).
- Prime factor 3: The smallest power is \(1\) (from \(3^2\), \(3^2\), and \(3^1\)).
- The prime factor 5 is not present in all the numbers.

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

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