A factor tree of 60. 60 branches to 4 and 15. 4 branches to 2 and 2. 15 branches to 3 and 5.
60 = 2 × 3 × 5
What is Darius’s error?
Darius should have started the factor tree with 2 × 30.
Darius did not complete the factorization; 5 is a composite number.
Darius should have expressed 15 as 5 × 5, not 3 × 5.
Darius should have expressed 60 as 22 × 3 × 5, not 2 × 3 × 5.
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Darius's prime factorization of 60 is incorrect. The correct prime factorization of 60 is \(2^2 \times 3^1 \times 5^1\).
The error in Darius's work is that he did not express 60 in terms of its full prime factorization, which includes the exponent for the factor 2.
Thus, the correct answer to identify Darius's error is:
Darius should have expressed 60 as \(2^2 \times 3 \times 5\), not \(2 \times 3 \times 5\).
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