Determine the highest common factor (HCF) of $48$ and $80$ using prime factorisation.

medium 2 marks Class 6 · Mathematics · Knowing Our Numbers

Answer

16

The correct answer is $16$ — Hence the HCF of $48$ and $80$ is $16$ .

Step-by-step solution

Prime‑factorise $48$ : $48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^{4} \times 3$ .
Prime‑factorise $80$ : $80 = 2 \times 2 \times 2 \times 2 \times 5 = 2^{4} \times 5$ .
Identify common prime factors with the lowest exponent: only $2$ is common, with exponent $4$ .
Compute the product of the common factors: $2^{4} = 16$ .
Hence the HCF of $48$ and $80$ is $16$ .

Common mistake: Using the minimum exponent instead of the lowest common power for HCF calculation

Concept tested: HCF using prime factorisation