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**Factors
and Multiples**

###
**Factors**

A set of numbers which divides a particular number
without leaving any remainder is called the

**factors**of that particular number. For example 1, 2, 3, 4, 6 and 12 can divide 12 without leaving any remainder, so 1, 2, 3, 4, 6 and 12 are the factors of 12.
12 ÷

**1**= 12
12 ÷

**2**= 6
12 ÷

**3**= 4
12 ÷

**4**= 3
12 ÷

**6**= 2
12 ÷

**12**= 1
We write this set of numbers in symbolic form as given
below.

**F**

_{12}= {1, 2, 3, 4, 6, 12}###
**Multiples**

**Multiples**of a number are the set of numbers which are obtained by multiplying the number with the whole numbers. For example 0, 3, 6, 9, 12, 15, 18, … are the the set of multiples of 3.

3 × 0 =

**0**
3 × 1 =

**3**
3 × 2 =

**6**
3 × 3 =

**9**
3 × 4 =

**12**and so on.
We write this set of numbers in symbolic form as given
below.

**M**

_{3}= {0, 3, 6, 9, 12, 15, 18, …}###
*Workout
Examples*

*Workout Examples*

*Example 1: Find the factors of 18.*

*Solution:*

*Here,*

*Factors of 18 are 1,2,3,6,9 and 18.*

*∴*

*F*_{18}= {1, 2, 3, 6, 9, 18}

*Example 2: Find the multiples of 4 up to 20.*

*Solution:*

*Here,*

*Multiples of 4 up to 20 are 0, 4, 8, 12, 16 and 20.*

*∴*

*M*_{4}= {0, 4, 8, 12, 16, 20}

*Example 3: Write the common factors of 12 and 16.*

*Solution:*

*Here,*

*Factors of 12, F*_{12}= {1, 2, 3, 4, 6, 12}

*Factors of 16, F*_{16}= {1, 2, 4, 8, 16}

*∴*

*Common factors of 12 and 16 = {1, 2, 4}*

*You can comment your questions or problems regarding factors and multiples here.*

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