Learning Objectives of the chapter Factors and Multiples for Class 4

At the end of this chapter you will be able to:

Multiples Of A Number

Below I am giving some examples of multiples of numbers from 2 to 9.

• Multiple of 2:
  2, 4, 6, 8, 10, 12, 14, 16, 18, 20
  
  
• Multiple of 3:
  3, 6, 9, 12, 15, 18, 21, 24, 27, 30
  
  
• Multiple of 4:
  4, 8, 12, 16, 20, 24, 28, 32, 36, 40
  
  
• Multiple of 5:
  5, 10, 15, 20, 25, 30, 35, 40, 45, 50
  
  
• Multiple of 6:
  6, 12, 18, 24, 30, 36, 42, 48, 54, 60
  
  
• Multiple of 7:
  7, 14, 21, 28, 35, 42, 49, 56, 63, 70
  
  
• Multiple of 8:
  8, 16, 24, 32, 40, 48, 56, 64, 72, 80
  
  
• Multiple of 9:
  9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Also Read: Roman Numerals chapter for Class 4

Now, let see the following example.

12 = 1 x 12 or 12 = 12 x 1

12 = 2 x 6 or 12 = 6 x 2

12 = 3 x 4 or 12 = 4 x 3

Here, we can say that 12 is a multiple of 1, 2, 3, 4, 6 and 12.

Let's take an another example.

18 = 1 x 18 or 18 = 18 x 1

18 = 2 x 9 or 18 = 9 x 2

18 = 3 x 6 or 18 = 6 x 3

Thus, 18 is a multiple of 1, 2, 3 and 6

Properties of Multiples

(1) 6 x 1 = 6, 9 x 1 = 9, 15 x 1 = 15

In the above example, you can see that,

6 is a multiple of 6 and 1, 9 is a multiple of 9 and 1, 15 is a multiple of 15 and 1.

Thus, every number is a multiple of itself and 1.

(2) 18 is a multiple of 1, 2, 3, 6 and 18.

See carefully that 18 is greater than 1, 2, 3 and 6. And it is equal 18.

Thus, multiple of a number is always greater than or equal to the number itself.

(3) Let's take a number 7. To find its multiple, we can multiply 7 by higher and higher numbers to get more and more multiples. Thus, we can get uncountable number of multiples.

Thus, a number has uncountable number of multiples and there is no largest multiple of a number.

From the above example you can see that,

1. Every number is a multiple of number 1.
   
   
2. Every number is a multiple of itself.
   
   
3. A multiple of a number is always greater than or equal to the number itself.
   
   
4. To find multiple of a number we can multiply it by 1, 2, 3, 4, 5, 6, ...
   
   
5. A number has uncountable number of multiples.
   
   
6. There is no largest multiple of number as we can multiply a number by any number.

Exercise on Multiples

Factors Of A Number

A Factor of a number divides the number without leaving a remainder.

Let's see an example below.

18 is a multiple of 1, 2, 3, 6 and 18.

If we divide 18 by 1, 2, 3, 6 or 18, no remainder is left. That means, we get 0 as remainder.

Thus, we can say that 1, 2, 3, 6 and 18 are factors of 18.

We can also find factor by using multiplication.

Let's take another example.

2 x 9 = 18, here, 2 and 9 are factors of 18.

4 x 7 = 28, here, 4 and 7 are factors of 28.

5 x 6 = 30, here, 5 and 6 are factors of 30.

REMEMBER

• When two or more numbers are multiplied we get a product.
• The product is a multiple of each of the numbers multiplied.
• Each number is a factor of the product.
  
  For example, 3 x 8 = 24, here, 24 is the product.
  Or we can say, 24 is the multiple of both 3 and 8.
  Both 3 and 8 are factors of 24.

Properties of Factors

(1) 1 can divide any number. Yes, any number.

Thus, 1 is a factor of every number.
Also, 1 is the smallest factor of every number.

(2) 9 is a multiple of 1, 3 and 9.

See carefully that 1, 3 and 9 are factors of 9. 

So, every number is a factor of itself.

(3) A number does not have uncountable number of factors. In other words, it has limited number of factors.

For example,

12 has 5 factors which are 1, 2, 3, 4 and 12.

15 has 4 factors which are 1, 3, 5 and 15.

(4) A factor of a number is either equal to or smaller than the number. The biggest factor of a number is the number itself.

Let's take the same example as above.

The factors of 15 are 1, 3, 5 and 15.

Thus, all the factors 1, 3, 5 and 15 are either equal to or smaller than 15. Also, 15 is the biggest factor of 15.

Exercise on Factors

Even Numbers

A number which is a multiple of 2 is called an even number.
For example, 2, 4, 6, 8, 10, 12, 14, ...

Odd Numbers

A number which is not a multiple of 2 is called an odd number.
For example, 1, 3, 5, 7, 9, 11, 13, ...

Prime Numbers

Numbers which have only two factors, 1 and the number itself, are called Prime numbers.
For example, 2, 3, 5, 7, 11, 13, 17, 19 are examples of prime numbers.

Composite Numbers

Numbers which have more than two factors are called Composite numbers.
For example, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20 are examples of composite numbers.

Exercise on Even, Odd, Prime and Composite Numbers

Common Factors

We already know how to find factors of a number. Now let's learn how to find common factors of numbers with the following example.

Exampe 1: Find the common factors of 15 and 21.

Factors of 15 are 1, 3, 5 and 15

Factors of 21 are 1, 3, 7 and 21

Common factors of 15 and 21 are 1 and 3.

Exampe 2: Find the common factors of 27 and 45.

Factors of 27 are 1, 3, 9 and 27

Factors of 45 are 1, 3, 5, 9, 15 and 45

Common Factors of 27 and 45 are 1, 3 and 9.

Highest Common Factors (HCF)

Example 1: Let's take the example 1 above and find the highest common factor of 15 and 21.

The common factors of 15 and 21 are 1 and 3.

Here, the highest common factors of 15 and 21 is 3.

Example 2: Find HCF of 27 and 45.

Common factors of 27 and 45 are 1, 3 and 9.

Thus, HCF of 27 and 45 is 9.

Example 3: Find HCF of 12, 16 and 24.

Factors of 12 are 1, 2, 3, 4, 6 and 12

Factors of 16 are 1, 2, 4, 8 and 16

Factors of 24 are 1, 2, 3, 4, 6, 12 and 24

Common factors of 12, 16 and 24 are 1, 2 and 4.

Thus, HCF of 12, 16 and 24 is 4.

Example 4: Find HCF of 4 and 16.

In this example, please note that 4 is a factor of 16.

Factors of 4 are 1 and 4

Factors of 16 are 1, 4 , 8 and 16

Common factors of 4 and 16 are 1 and 4.

Thus, HCF of 4 and 16 is 4.

If a number is a factor of another number, then their HCF is the smaller of the two numbers.

In above example, 4 is a factor of 16. Also, out of 4 and 16, 4 is the smaller number, therefore, 4 is the HCF of 4 and 16.

Example 5: Find the HCF of 8 and 15.

Factors of 8 are 1, 2, 4 and 8

Factors of 15 are 1, 3, 5 and 15

Common factors of 8 and 15 is only 1.

Thus, there is no highest common factor. Also, two numbers which have only 1 as the common factor are called coprime.

Therefore, 8 and 15 are coprime.