Express $540$ as a product of its prime factors.[1] Explain why $540$ is not a cubic number.[1]

Question

Express $540$ as a product of its prime factors.[1] Explain why $540$ is not a cubic number.[1] Find the smallest positive integer $k$ such that $540k$ is a perfect square.[1] Written as the product of its prime factors, $84={{2}^{2}}\times 3\times 7$. Find the highest common factor (HCF) and lowest common multiple (LCM) of $84$ and $540$, giving your answer in index notation.[2]

Accepted Answer

(a) $2^2\times3^3\times5$. (b) The exponents of 2 and 5 are not multiples of 3. (c) $15$. (d) HCF $=2^2\times3=12$, LCM $=2^2\times3^3\times5\times7=3780$.

2023 AISS S3 EM P1 Q7

2023 AISS S3 EM P1 Q7

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