Answered

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NAME: ______________

1. Ava wants to find the Greatest Common Factor (GCF) of 32 and 12. She started by finding the prime factorization of each number but then she forgot the next step. Below is Ava's work:

[tex]\[
\begin{array}{l}
32 = 2 \times 2 \times 2 \times 2 \times 2 \\
12 = 2 \times 2 \times 3
\end{array}
\][/tex]

What should Ava do next to find the GCF of 32 and 12?

A. Multiply [tex]\(2 \times 2\)[/tex]
B. Multiply [tex]\(2 \times 3\)[/tex]
C. Multiply [tex]\(2 \times 2 \times 2 \times 2\)[/tex]
```



Answer :

GinnyAnswer
To find the Greatest Common Factor (GCF) of 32 and 12, Ava should follow these steps:

1. Begin with the prime factorizations she already determined:
[tex]\[ 32 = 2 \times 2 \times 2 \times 2 \times 2 \][/tex]
[tex]\[ 12 = 2 \times 2 \times 3 \][/tex]

2. Identify the common prime factors between the two numbers. The common prime factors are those that appear in the factorizations of both numbers. From the prime factorizations, we see that both 32 and 12 have the prime factor 2.

3. Determine the lowest power of each common prime factor. Here, the common prime factor is 2. In the factorization of 32, 2 appears five times, and in the factorization of 12, 2 appears twice. We take the lowest number of appearances, which is twice.

4. Multiply these lowest common powers together to find the GCF:
[tex]\[ 2 \times 2 = 4 \][/tex]

Given the options:
A. Multiply [tex]\(2 \times 2\)[/tex]
B. Multiply [tex]\(2 \times 3\)[/tex]
C. Multiply [tex]\(2 \times 2 \times 2 \times 2\)[/tex]

The correct answer for Ava to find the GCF is:
A. Multiply [tex]\(2 \times 2\)[/tex]

Thus, the GCF of 32 and 12 is 4.

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