2026 PCSS P1 Q9

2026 PCSS P1 Q9

Secondary 4
3 marks

Written as a product of its primes factors, \(72=2^3\times3^2\).

  1. The number \(72\times45\times\dfrac pq\) is a perfect square where \(p\) and \(q\) are prime numbers.
    Find the smallest value of \(\dfrac pq\).[2]
  2. Given that the highest common factor of 72 and \(m\) is \(2^2\times3\), write down the two smallest possible value of \(m\).[1]

Solution:

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Answer:(a) \(\dfrac25\), with \(p=2,q=5\) (b) 12 and 60

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