## Factors and Multiples Examples

### Factor :

if we have two numbers and first number exactly divisible by the second number then the second number is known as factor of first number. If second number is exactly divisible by the first number , then first number is known as factor of second number.

**Factors example :**

If we have to check whether 4 is a factor of 64 or not, then we will divide 64 by 4 and if we are getting remainder 0 , then 4 will be factor of 64 otherwise not. We should always remember that factor of any number always less than or equal to the number. Smallest factor of any number is 1 and greatest factor of any other number is that number itself.

### Properties of factors :

- 1 is a factor of every non zero number.
- Every non zero number is the factor of itself.
- Factor of any number always less than or equal to the number.
- Every non zero number is a factor of 0.
- Every non zero number except 1 has at least two factors 1 and number itself.

**Example 1 : Find the factors of 8 , 12, 16 , 18 and 20**

Solution : factors of 8 = 1, 2, 4 ,8

Factors of 12 = 1,2,3,4,6,12

Factors of 16 = 1,2,4,8,16

Factors of 18 = 1,2,3,6,9,18

Factors of 20 = 1,2,4,5,10,20

## Multiple :

if we have two numbers and first number is exactly divisible by the second number then the first number is known as Multiple of second number. If second number is exactly divisible by the first number , then second number is known as Multiple of first number. For example:

If we have to check whether 64 is a multiple of 4 or not , then we will divide 64 by 4 and if we are getting remainder 0, then 64 will be Multiple of 4 otherwise not. We should always remember that Multiple of any number always greater than or equal to the number. Smallest multiple of any number itself. There is no greatest multiple of any number.

### Properties of Multiple :

- Every number is a multiple of 1.
- 1 is a multiple of every number.
- Every number is a multiple of itself.
- Multiple of any other number always greater than or equal to the number.
- There is no limit of multiples i.e. we can find unlimited of any number.

**Multiple of 4 : all numbers which are exactly divisible by 4.4,8,12,16,20,24,28,32,36,40,44…….**

**Example 2 : write the first 8 multiple each of the following: 3, 5,8,12,15.Solution :**

Multiple of 3 = 3,6,9,12,15,18,21,24

Multiple of 4 = 4,8,12,16,20,24,28,32

Multiple of 8 = 8,16,24,36,40,48,56,64

Multiple of 12 = 12,24,36,48,72,84,96

Multiple of 15 = 15,30,45,60,75,90,105,120

#### Natural Numbers

The numbers 1,2,3,4,5,6….. are Natural Numbers . Smallest natural numbers is

- There is no greatest natural number.

#### Whole Numbers

The numbers 0 ,1,2,3,4,5,6,7… are whole Numbers. Smallest whole number is

- There is no greatest whole number.

#### Even Numbers

The numbers which are divisible by 2 are known as even Numbers. For example : 2,4,6,8,10 etc. Smallest even number is 2 and there is no greatest even number.

#### ODD Numbers

The numbers which are not divisible by 2 are known as odd numbers. For example : 1, 3,5,7,9 etc. Smallest odd number is 1 and there is no greatest odd number.

#### Prime numbers

The numbers , having exactly two factors 1 and itself , are known as prime numbers. For example: 2,3,5,7,11,13,17,19 etc. 2 is the smallest prime numbers 1 is not a prime numbers.

#### Composite numbers

The number which are having more than two factors are known as composite numbers. For example : 4,6,8,12 etc.

#### Coprime Numbers

Two numbers are known as co-prime if they have only 1 as common factors . For example : 2 and 3 , 3 and 5 ,5 and 7 etc.

## Method of find prime numbers between 1 and 100:

Step -1 : put a cross on 1

Step-2 : put cross on all multiple of 2 except 2.

Step-3: put cross on all multiple of 3 except 3.

Step-4 : put cross on all multiple of 5 except 5 .

Step-5 : put cross on all multiple of 7 except 7

Step -6 : Encircle all the numbers which are not crossed.