Question

amar tried to find the gcf of 36 and 54. his work is shown below.

factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
factors of 54: 1, 2, 6, 9, 27, 54

the gcf is 9.

what was amars error?

• the student missed two factors for the number 54.
• the student listed multiples of each number instead of factors.
• the student missed two factors for the number 36.
• the student selected the least common factor.

Explanation:

Analyze the student's work for 36

The student listed the factors of 36 as: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Using the Factors knowledge point, we verify:
\(1 \times 36 = 36\)
\(2 \times 18 = 36\)
\(3 \times 12 = 36\)
\(4 \times 9 = 36\)
\(6 \times 6 = 36\)
All factors of 36 are correctly listed.

Analyze the student's work for 54

The student listed the factors of 54 as: 1, 2, 6, 9, 27, 54.
Using the Factors knowledge point, we find the complete set of factors of 54:
\(1 \times 54 = 54\)
\(2 \times 27 = 54\)
\(3 \times 18 = 54\)
\(6 \times 9 = 54\)
The complete list is: 1, 2, 3, 6, 9, 18, 27, 54.
Comparing this to Amar's list, he missed 3 and 18.

Identify the error

Amar missed two factors (3 and 18) for the number 54.
This matches the first option.

Evaluate the other options

• "The student listed multiples...": Incorrect, they listed factors.
• "The student missed two factors for 36": Incorrect, 36's list is complete.
• "The student selected the least common factor": Incorrect, the primary error is in listing the factors.

Answer:

• The student missed two factors for the number 54. (Correct answer)
• The student listed multiples of each number instead of factors.
• The student missed two factors for the number 36.
• The student selected the least common factor.