The answer
\(N = 8000\)
O-Level E-Math 2024 Paper 1 Question 19 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 19 of the O-Level E-Math 2024 Paper 1. It tests prime factorisation, in the Numbers & the four operations area. It is worth 2 marks. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
Compare each prime, using HCF = lowest power and LCM = highest power between \(720\) and \(N\). - Prime \(2\): \(720\) has \(2^4\). HCF has \(2^4 \Rightarrow N\) has at least \(2^4\); LCM has \(2^6 \Rightarrow N\) supplies \(2^6\). So \(N\) has \(2^6\). - Prime \(3\): \(720\) has \(3^2\). HCF has \(3^0 \Rightarrow N\) has \(3^0\) (no factor of 3); LCM has \(3^2\), supplied by \(720\). So \(N\) has no factor of \(3\). - Prime \(5\): \(720\) has \(5^1\). HCF has \(5^1 \Rightarrow N\) has at least \(5^1\); LCM has \(5^3 \Rightarrow N\) supplies \(5^3\). So \(N\) has \(5^3\).
Hence \(N = 2^6 \times 5^3 = 64 \times 125 = 8000\).
Answer: \(N = 8000\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a prime factorisation question from Numbers & the four operations, worth 2 marks.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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