**What are Factors?**

Factors of a number are integers that can be multiplied together to yield that specific number. Every whole number has at least two factors: 1 and the number itself. For instance, the factors of 6 are 1, 2, 3, and 6, as 1 × 6 = 6 and 2 × 3 = 6.

**Characteristics of Factors**

**Prime Factors:**- Prime factors are factors that are prime numbers. The prime factorization of a number involves expressing it as the product of its prime factors.

**Factor Pairs:**- Factors often come in pairs. For instance, the factors of 12 are 1, 2, 3, 4, 6, and 12, forming pairs such as (1, 12), (2, 6), and (3, 4).

**How to Find Factors of a Number?**

**Finding Factors of a Number: A Step-by-Step Guide**

**Step 1: Start with 1 and the Number Itself**

- Every whole number has at least two factors: 1 and the number itself.

**Step 2: Check for Small Factors**

- Begin with the smallest possible factor, 2.
- Test if the number is divisible by 2. If yes, 2 is a factor.
- Repeat this process with 3, 4, 5, and so on, until the quotient becomes greater than the divisor.

**Step 3: Factor Pairs**

- As you identify factors, note them down.
- Look for factor pairs. For example, if 3 is a factor, then \(\frac{n}{3}\) is also a factor.

**Step 4: Stop at the Square Root**

- You only need to check factors up to the square root of the number.
- If a number has a factor larger than its square root, it must also have a corresponding factor smaller than the square root.

**Step 5: List All Factors**

- Compile a list of all the factors you have found.

**Example: Finding Factors of 24**

- Start with 1 and 24.
- Check for factors: 2, 3, 4, 6, and 8.
- Factor pairs: (1, 24), (2, 12), (3, 8), (4, 6).
- Stop at the square root of 24, which is approximately 4.9.
- List all factors: 1, 2, 3, 4, 6, 8, 12, and 24.

**Tips:**

- Use divisibility rules for common divisors (e.g., divisibility by 2, 3, 5).
- Be systematic in testing potential factors.
- Factorization can be helpful in identifying factors quickly.

**Examples of Factors**

**Factors of 8:**- The factors of 8 are 1, 2, 4, and 8.
- Factor pairs: (1, 8) and (2, 4).

**Factors of 15:**- The factors of 15 are 1, 3, 5, and 15.
- Factor pairs: (1, 15) and (3, 5).