Question

The HCF of 960 and 432 is :

• A. 48
• B. 54
• C. 72
• D. 36

Hint:

Euclid's division algorithm is generally faster for larger numbers compared to prime factorization, as finding prime factors of large numbers can be time-consuming.
Always write down the steps of division clearly to avoid simple arithmetic mistakes.

Answer 1

The Correct Option is A

Step 1: Break both numbers into prime factors.
\[ 960 = 2^6 \times 3 \times 5, \qquad 432 = 2^4 \times 3^3 \]
Step 2: Pick the lowest power of every common prime.
The common primes are 2 and 3. The lower power of 2 is $2^4$, and the lower power of 3 is $3^1$.
Step 3: Multiply those lowest powers together.
$\text{HCF} = 2^4\times3^1 = 16\times3 = 48$.
\[ \boxed{48} \]