# Multiples of 3

View Notes

### Introduction to Multiples of 3

When we talk about multiples of 3 it is the set of all those numbers which can be expressed in the form of 3n or in other words the number which gives the remainder zero when it is divided by 3 is called a multiple of three.All the multiples of three must contains 3 as its one of the factor.

For example, number 18 can be expressed as 2 × 3 × 3 thus we can see that 3 is one of its  factors also it is expressed in terms of 3n so this is multiple of three. Thus, in other words we can say that all those numbers which can be divided by three or are products of 3 and any number is defined as a multiple of 3.

## Calculation of Multiples of 3

The multiples of number 3 can be calculated and by multiplying integers. For example in order to calculate the multiples of 3 we will use product of 3 with the natural numbers 1, 2, 3, .......... and thus will get 3 x 1, 3 x 2, 3 x 3, 3 x 4, 3 x 5, etc., which equal 3, 6, 9, 12, 15, etc. All the multiples of 3 that come in the table of three are multiples of 3 i.e. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30……………….etc. Thus multiples of 3 is expressed as 3p where p is integer.

### Set of Multiples of 3

Multiples of 3 can be written in form set in roster or tabular form as well as in set builder for.

1) In roster or tabular form the numbers of set are written within bracket separated by the commas so multiples of three will be written as

{0, 3, 6, 9, 12,...}

2) In set Builder form elements of set are written with their properties thus the multiples of 3 will be written as

{x:x = 3n,n ∈ W, where W is whole number}

### Meaning of Multiples:

The multiple of a number can be defined as the number that can be written as the product of a given number and some other natural number. Multiples of the numbers can be observed in the multiplication table. Multiples of natural numbers some numbers are as given below:

For e.g., multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and so on Hence, multiples of 2 will be even numbers and will end with 0, 2, 4, 6 or 8.

The multiples of the number 3 are 3, 6, 9, 12, 15, 18, 21,24,.............. and so on.

The multiples of the number 5 are 5, 10, 15, 20, 25, ,.............. and so on.

All the multiples of 5 will have the last digit as 0 or 5.

From the above given examples we can say that multiples of 2, the number 2 can be multiplied by infinite numbers to find the “n” number of multiples.

### Difference Between Factors and Multiples:

The exact divisors of the given number can be defined as the factor of the given number while the multiples of the number are defined as the numbers obtained when multiplied by other numbers.

The number of factors of any number is always finite while the number of multiplies of the number is infinite.

The operation which is used to find the factors of any number is a division while the operation used to find the multiples of a given number is called the multiplication.

The result or the outcome of the factors any given number will always be less than or equal to the given number while the result or the outcome of the multiples should be greater than or equal to the given number.

Now, let us assume an example:

3 × 4 = 12

Here, 3 and 4 are the factors of 12,

12 is multiple of 3 and 4

Thus, we can conclude that if X and Y are two numbers and;

• X is a factor of Y, if  X divides Y.

• Y is a multiple of X, if Y is divisible by X.

We know that the number 1 divides every integer thus it is the common factor of each and every integer and also every number is divisible by 1 and every number is a multiple of 1.