The prime factorization of a number is `2xx3xx13`. What is the number and what are all of its factors?

Answer

To solve the problem step by step, we will first determine the number from its prime factorization and then find all of its factors.

### Step 1: Determine the Number from Prime Factorization
The prime factorization given is \(2 \times 3 \times 13\).

To find the number, we multiply these prime factors together:
\[ \text{Number} = 2 \times 3 \times 13 \]

Calculating this step-by-step:
1. First, multiply \(2\) and \(3\):
\[ 2 \times 3 = 6 \]
2. Now, multiply the result by \(13\):
\[ 6 \times 13 = 78 \]

Thus, the number is \(78\).

### Step 2: Find All Factors of the Number
To find all factors of \(78\), we need to determine all the integers that divide \(78\) without leaving a remainder.

1. Start with \(1\):
- \(78 \div 1 = 78\) (so \(1\) and \(78\) are factors)

2. Check \(2\):
- \(78 \div 2 = 39\) (so \(2\) and \(39\) are factors)

3. Check \(3\):
- \(78 \div 3 = 26\) (so \(3\) and \(26\) are factors)

4. Check \(6\):
- \(78 \div 6 = 13\) (so \(6\) and \(13\) are factors)

5. Check \(13\) (already counted with \(6\)):
- \(78 \div 13 = 6\) (already counted)

6. Check \(26\) (already counted with \(3\)):
- \(78 \div 26 = 3\) (already counted)

7. Check \(39\) (already counted with \(2\)):
- \(78 \div 39 = 2\) (already counted)

8. Check \(78\) (already counted with \(1\)):
- \(78 \div 78 = 1\) (already counted)

Now, we compile all the unique factors we found:
- The factors of \(78\) are: \(1, 2, 3, 6, 13, 26, 39, 78\).

### Final Answer
The number is \(78\) and its factors are \(1, 2, 3, 6, 13, 26, 39, 78\).

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