Question

The highest common factor (HCF) of 72, 108 and 180 is

• A. 18
• B. 36
• C. 24
• D. 12

Hint:

Use the lowest power of each shared prime factor across all three numbers.

Answer 1

The Correct Option is B

Step 1: Prime factorise each number.
\(72=2^3\times3^2\), \(108=2^2\times3^3\), \(180=2^2\times3^2\times5\).
Step 2: Take the lowest power of each common prime.
Common primes are 2 and 3: lowest powers \(2^2\) and \(3^2\).
Step 3: Multiply.
\(2^2\times3^2=4\times9=36\).
\[\boxed{36}\]