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The provided text seems to be a mixture of valid mathematical operations and nonsensical statements, along with a malformed table. Let's rewrite it to make it coherent and understandable.

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Solve the following division problems and classify the results as prime or composite numbers:

[tex]\[
6 \div 1 = 6 \quad
6 \div 3 = 2
\][/tex]

(Note: Division by zero is undefined, so [tex]\( 6 \div 0 = \)[/tex] is not a valid operation.)

[tex]\[
\begin{array}{c|c}
\text{Number} & \text{Prime/Composite} \\
\hline
12 & \\
14 & \\
3 & \text{Prime} \\
31 & \text{Prime} \\
20 & \\
45 & \\
17 & \text{Prime} \\
7 & \text{Prime} \\
\end{array}
\][/tex]

Complete the table by classifying each number as either prime or composite.
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Answer :

GinnyAnswer
Sure, let's classify the given numbers into prime and composite groups, following logical mathematical steps.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

A composite number is a natural number that has positive divisors other than 1 and itself.

Given the list of numbers: 12, 14, 3, 31, 20, 45, 17, and 7, we will determine which are prime and which are composite.

1. 12:
- Divisors: 1, 2, 3, 4, 6, 12
- Composite

2. 14:
- Divisors: 1, 2, 7, 14
- Composite

3. 3:
- Divisors: 1, 3
- Prime

4. 31:
- Divisors: 1, 31
- Prime

5. 20:
- Divisors: 1, 2, 4, 5, 10, 20
- Composite

6. 45:
- Divisors: 1, 3, 5, 9, 15, 45
- Composite

7. 17:
- Divisors: 1, 17
- Prime

8. 7:
- Divisors: 1, 7
- Prime

Based on this analysis, we can now classify the numbers into prime and composite categories.

Prime numbers: 3, 31, 17, 7

Composite numbers: 12, 14, 20, 45

So, the classification of the numbers into prime and composite groups is:

- Prime numbers: [3, 31, 17, 7]
- Composite numbers: [12, 14, 20, 45]