Discuss Types of Numbers and Factors of a Number. Include explanations, examples, differentiation, methods to find factors, and identification of prime/composite numbers.

Types of Numbers

Explanation of 4 Types of Numbers:

1. Even numbers: Integers divisible by 2 with remainder 0.
   Examples: $2, 4, 6, 8, 10$.

2. Odd numbers: Integers not divisible by 2.
   Examples: $1, 3, 5, 7, 9$.

3. Prime numbers: Natural numbers greater than 1 with exactly 2 distinct positive factors (1 and itself).
   Examples: $2, 3, 5, 7, 11$.

4. Composite numbers: Natural numbers greater than 1 that are not prime (more than 2 positive factors).
   Examples: $4, 6, 8, 9, 10$.

Examples and Differentiation:

• 2: Even and prime.
• 3: Odd and prime.
• 4: Even and composite (factors: 1,2,4).
• 9: Odd and composite (factors: 1,3,9).

Numbers can have multiple types (e.g., 6 is even and composite).

Factors of a Number

Definition and Explanation of Factors:
Factors of a number $n$ are positive integers $d$ such that $n \div d$ gives quotient $q$ with remainder 0 ($n = d \times q$).
Example for $n=12$:
Factors: 1,2,3,4,6,12.

$$12 \div 1 = 12, \quad 12 \div 2 = 6, \quad 12 \div 3 = 4,$$ $$12 \div 4 = 3, \quad 12 \div 6 = 2, \quad 12 \div 12 = 1.$$

Method to Find Factors:
Use pair method up to $\sqrt{n}$. Example: $n=36$, $\sqrt{36}=6$.