Step 1: Pick a different route.
The solution on the other tab found the HCF of 960 and 432 by breaking both numbers into prime factors. Here we get the same answer using Euclid's division algorithm, which never needs a prime factor tree at all.
Step 2: Recall the rule.
Euclid's division lemma says that for two positive integers $a$ and $b$ with $a > b$, we can write $a = bq + r$ where $0 \leq r < b$. The rule that makes this useful is: $\text{HCF}(a, b) = \text{HCF}(b, r)$. So we keep replacing the larger number by the remainder until the remainder becomes 0. The last non zero divisor at that point is the HCF.
Step 3: Apply it to 960 and 432.
Divide the larger number by the smaller one.
\[ 960 = 432 \times 2 + 96 \]
Now divide 432 by the remainder 96.
\[ 432 = 96 \times 4 + 48 \]
Now divide 96 by the new remainder 48.
\[ 96 = 48 \times 2 + 0 \]
The remainder has become 0, so we stop here.
Step 4: Read off the HCF.
The last divisor we used before getting a remainder of 0 was 48. So the HCF of 960 and 432 is 48, and it took only three short divisions instead of breaking both numbers all the way down into primes. This matches option (A).
\[ \boxed{\text{HCF}(960, 432) = 48} \]