Question 1
A student uses a factor tree to factorise 60 and another student uses repeated division. Which statement best describes what should happen?No clue? Show me the answer
Correct answerCorrect!
IncorrectStep-by-step walkthrough
Choose a solution method
Method #1Direct ApproachStep 1: Recall the uniqueness of prime factorisation
A fundamental property of prime factorisation is that every composite number has exactly one prime factorisation (ignoring the order of factors). This is sometimes called the Fundamental Theorem of Arithmetic.
Step 2: Apply this to both methods
Whether you use a factor tree starting with or repeated division starting from 2, you will always end up with the same set of prime factors: .
Step 3: Choose the correct statement
The correct answer is that both methods must produce the same prime factorisation. The method used does not change the result.
Method #2Process of EliminationStep 1: Identify the concept being tested
This question tests whether you know that prime factorisation is unique — every composite number has exactly one prime factorisation.
Step 2: Eliminate 'The factor tree method may give a different factorisation'
This is false. While different starting pairs in a factor tree may look different during working, they always produce the same final set of prime factors.
Step 3: Eliminate 'Repeated division always gives more prime factors'
This is false. Both methods count the same prime factors — neither adds or removes primes.
Step 4: Eliminate 'The results can differ because of branch choice'
Although the order in which you split branches varies, the final collection of prime factors is always identical.
Step 5: Select the correct answer
Both methods must produce the same prime factorisation — this is guaranteed by the uniqueness of prime factorisation.
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