Question

amar found the gcf of 36 and 54. his work is shown here.

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 factors of 36

The factors of 36 are listed as:
\(1, 2, 3, 4, 6, 9, 12, 18, 36\)
These are all correct and complete.

Analyze the factors of 54

The factors of 54 are listed as:
\(1, 2, 6, 9, 27, 54\)
The actual factors of 54 are:
\(1, 2, 3, 6, 9, 18, 27, 54\)
Comparing the lists, Amar missed the factors \(3\) and \(18\).
This means the student missed two factors for the number 54.

Evaluate the options

• "The student missed two factors for the number 54." (Correct, missed 3 and 18)
• "The student listed multiples of each number instead of factors." (Incorrect)
• "The student missed two factors for the number 36." (Incorrect)
• "The student selected the least common factor." (Incorrect)

Answer:

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