Prime Decomposition and Cube Multipliers

Prime Decomposition and Cube Multipliers

IP 1
5 marks
  1. Find the prime factors of \(800\) and \(1125\), 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 \(800\) and \(1125\),[1]
    2. lowest common multiple of \(800\) and \(1125\).[1]
  3. Write down the smallest positive integer value of \(q\) such that \(\sqrt[3]{1125q}\) is a whole number.[1]

Solution:

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Answer:(i) \(800=2^5\times5^2\), \(1125=3^2\times5^3\) (ii)(a) \(5^2\) (b) \(2^5\times3^2\times5^3\) (iii) \(q=3\)

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