Prime Factors, HCF and Cube Completion

Prime Factors, HCF and Cube Completion

IP 1
5 marks
  1. Find the prime factors of \(360\) and \(675\), giving your answers in index form.[2]
  2. Using the answers obtained in part (i), state the following, leaving your answers in index form.
    1. highest common factor of \(360\) and \(675\),[1]
    2. lowest common multiple of \(360\) and \(675\).[1]
  3. Write down the smallest positive integer value of \(q\) such that \(\sqrt[3]{675q}\) is a whole number.[1]

Solution:

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Answer:(i) \(360=2^3\times3^2\times5\), \(675=3^3\times5^2\) (ii)(a) \(3^2\times5\) (b) \(2^3\times3^3\times5^2\) (iii) \(q=5\)

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