EXERCISE 3.2 Define with two examples of each: \( \begin{array}{ll}\text { (a) Factor } \\ \text { What is the sum of any two: } & \text { (b) Multiple } \\ \text { (a) Odd numbers } & \text { (b) Even numbers } \\ \text { Mathematics-6 } 34\end{array} \)

Let's define the terms "factor" and "multiple" and provide examples for each category. ### (a) Factor A factor of a number is an integer that can be multiplied by another integer to produce that number. In other words, if \( a \) is a factor of \( b \), then \( b \) can be expressed as \( b = a \times k \) for some integer \( k \). **Examples of Factors:** 1. **Factors of 12:** The factors of 12 are 1, 2, 3, 4, 6, and 12. For instance, \( 3 \) is a factor of \( 12 \) because \( 12 = 3 \times 4 \). 2. **Factors of 15:** The factors of 15 are 1, 3, 5, and 15. For example, \( 5 \) is a factor of \( 15 \) because \( 15 = 5 \times 3 \). ### (b) Multiple A multiple of a number is the product of that number and an integer. In other words, if \( a \) is a multiple of \( b \), then \( a = b \times k \) for some integer \( k \). **Examples of Multiples:** 1. **Multiples of 3:** The first few multiples of 3 are 3, 6, 9, 12, 15, etc. For example, \( 12 \) is a multiple of \( 3 \) because \( 12 = 3 \times 4 \). 2. **Multiples of 5:** The first few multiples of 5 are 5, 10, 15, 20, 25, etc. For instance, \( 20 \) is a multiple of \( 5 \) because \( 20 = 5 \times 4 \). ### Odd Numbers Odd numbers are integers that are not divisible by 2. They can be expressed in the form \( 2n + 1 \), where \( n \) is an integer. **Examples of Odd Numbers:** 1. **Example 1:** 1 (since \( 1 \div 2 \) leaves a remainder of 1) 2. **Example 2:** 3 (since \( 3 \div 2 \) leaves a remainder of 1) ### Even Numbers Even numbers are integers that are divisible by 2. They can be expressed in the form \( 2n \), where \( n \) is an integer. **Examples of Even Numbers:** 1. **Example 1:** 2 (since \( 2 \div 2 = 1 \) with no remainder) 2. **Example 2:** 4 (since \( 4 \div 2 = 2 \) with no remainder) ### Summary - **Factors:** - Factors of 12: 1, 2, 3, 4, 6, 12 - Factors of 15: 1, 3, 5, 15 - **Multiples:** - Multiples of 3: 3, 6, 9, 12, 15 - Multiples of 5: 5, 10, 15, 20, 25 - **Odd Numbers:** 1, 3 - **Even Numbers:** 2, 4