2026 RSS P1 Q23

2026 RSS P1 Q23

Secondary 4
5 marks
    1. Write 216 as a product of its prime factors.[1]
    2. The highest common factor of two numbers is 12.
      The lowest common multiple of the two numbers is 216.
      Both numbers are greater than 15.
      Find the two numbers.[2]
  2. Written as a product of its prime factors, \(1728=2^6\times3^3\).
    The number \(1728\div\dfrac{p^2}{q}\) is a perfect square, where \(p\) and \(q\) are prime numbers, \(p<q\).
    Find the value of \(p\) and of \(q\).[2]

Solution:

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Answer:(a)(i) \(2^3\times3^3\) (ii) 24 and 108 (b) \(p=2\), \(q=3\)

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