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Answer
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Solution
**Step 1: Prime Factorization**
We begin by finding the prime factorization of \(30\).
\[
30 = 2 \times 3 \times 5
\]
**Step 2: Identify All Factors**
The factors of \(30\) are all numbers that can be formed by multiplying one or more of its prime factors. This includes the product of none of the prime factors (which is \(1\)) and the product of all of them (which is \(30\)).
The factors are:
- \(1\) (by taking no prime factors)
- \(2\)
- \(3\)
- \(5\)
- \(2 \times 3 = 6\)
- \(2 \times 5 = 10\)
- \(3 \times 5 = 15\)
- \(2 \times 3 \times 5 = 30\)
**Final Answer**
The factors of \(30\) are:
\[
\{1, 2, 3, 5, 6, 10, 15, 30\}
\]
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Simplify this solution Beyond the Answer
The factors of 30 are the numbers that can be multiplied together in pairs to equal 30. These numbers include 1, 2, 3, 5, 6, 10, 15, and 30. Isn't it neat how factors work? If you pair them up, you have (1, 30), (2, 15), (3, 10), and (5, 6) all working together to create 30! And let's take a fun trivia twist! Did you know that knowing the factors of a number can be really helpful when you're trying to simplify fractions or perform division? Understanding these factors can also spice up your math game when playing number-related board games or solving puzzles. So, keep those factor friends handy!
