## This particular lesson is an important starting point for fractions. Knowing the factors and multiples of a number is very useful when you need to cancel down a fraction or bring fractions to a common denominator.

**Learning Objectives**

• What are factors

• How to find factors

• Divisibility rules

• What are multiples

• How to find multiples

Key words: factors, multiples, division rules,

**What are the factors?**

The factors of a number are all the numbers that divide into it

Imagine factors as all ingredients used to build the number:

**Take the example above:**

In order to build 75 we need do multiply 3, 2 and 5

To find out the factors of as number we need to divide the number applying the divisibility rules:

**Dividing by 2:** All even numbers are divisible by 2.

Example: all numbers ending in 0,2,4,6

**Dividing by 3**: Add up all the digits in the number and find out what the sum is. If the sum is divisible by 3, so is the number.

Example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

**Dividing by 4**: See if the last two digits in your number are divisible by 4.

Example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

**Dividing by 5**: Numbers ending in a 5 or a 0 are always divisible by 5.

Example: 25, 65, 200,

**Dividing by 6**: If the Number is divisible by 2 and 3 it is divisible by 6 also.

Example: 66; 30, 42

**Dividing by 8**: if the last 3 digits are divisible by 8, so is the entire number.

Example: 6008 – The last 3 digits are divisible by 8, therefore, so is 6008.

**Dividing by 9:** Almost the same rule and dividing by 3. Add up all the digits in the number, if the sum is divisible by 9, so is the number.

Example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

**Dividing by 10**: If the number ends in a 0, it is divisible by 10.

Example: 10, 100, 1000,

Finding the factors of a number

Just apply the divisibility rules using any of the next schemes above:

**Multiples of a number**

The concept of Multiple is the opposite to that of a

factor. If some number A is a factor of a number B, that

means that B is a multiple of A.

Any number has a set of multiples. These multiples are

that number multiplied by various integers. A number can

have infinity of multiples.

**Example**

The multiples of 3 are it’s time tables

3*0=0,

3*1=3,

3*2=6,

3*3=9

Some multiples of 12 : 24, 36, 48, 60

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