High School

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Darius created a factor tree and wrote the prime

factorization of 60 shown here.

What is Darius's error?

O Darius should have started the factor tree with 2 *

30.

60


O Darius did not complete the factorization: 5 is a

composite number

O Darius should have expressed 15 as 5 * 5. not 3*


O Darius should have expressed 60 as 22 x 3 x 5. not

2 x 3 x 5.

2

60 = 2 * 3x5

Darius created a factor tree and wrote the prime factorization of 60 shown here What is Darius s error O Darius should have started the

Answer :

Final answer:

Darius's prime factorization of 60 was incorrect. The correct prime factorization of 60 is 2^2 * 3 * 5, not 2 * 3 * 5. The error was in missing the second 2 in the prime factorization.

Explanation:

Darius is trying to find the prime factorization of the number 60. Prime factorization of any number is the representation of that number as a product of its prime factors. Looking at Darius's representation which is 2 * 3 * 5, he seems to have made an error.

He only used one 2, however, 60 is divisible by 2 twice, or in terms of prime factors we can say it has two 2's in its prime factorization.

In reality, the prime factorization of 60 is 22 * 3 * 5. Hence, Darius should have expressed 60 as 22 * 3 * 5, not as 2 * 3 * 5. His error was in not completely breaking down the factor tree, and recognizing that the 60 has two 2's in its prime factorization.

Learn more about Prime Factorisation here:

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Answer:

D

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