# Learning Objectives of the chapter Factors and Multiples for Class 4

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

• list the multiples of a number
• list the factors of a number
• calculate the HCF of two or more numbers
• calculate the LCM of two or more numbers
• use the prime factorisation method to find HCF and LCM

## 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

#### 20 is a multiple of 1, ____, ____, ____, 10 and 20.

20 = 1 x 20 or 20 x 1
20 = 2 x 10 or 10 x 2
20 = 4 x 5 or 5 x 4

Thus, 20 is a multiple of 1, 2, 4, 5, 10 and 20.

So, the answer would be 2, 4, 5.

#### 32 is a multiple of 1, ____, ____, ____, 16 and 32.

32 = 1 x 32 or 32 x 1
32 = 2 x 16 or 16 x 2
32 = 4 x 8 or 8 x 4

Thus, 32 is a multiple of 1, 2, 4, 8, 16 and 32.

So, the answer would be 2, 4, 8.

#### Find a number that is a multiple of both 5 and 8.

5 x 8 = 40
Thus, 40 is a multiple of both 5 and 8.

#### A multiple of a number can be equal to the number itself. (True / False)

True.
For example,
21 is a multiple of 1, 3, 7 and 21.
Thus, 21 is a multiple of itself also.

#### Every number is not a multiple of 1. (True / False)

False.
Every number is a multiple of 1.

## 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

#### 20 is a multiple of 1, ____, ____, ____, 10 and 20.

20 = 1 x 20 or 20 x 1
20 = 2 x 10 or 10 x 2
20 = 4 x 5 or 5 x 4

Thus, 20 is a multiple of 1, 2, 4, 5, 10 and 20.

So, the answer would be 2, 4, 5.

#### 32 is a multiple of 1, ____, ____, ____, 16 and 32.

32 = 1 x 32 or 32 x 1
32 = 2 x 16 or 16 x 2
32 = 4 x 8 or 8 x 4

Thus, 32 is a multiple of 1, 2, 4, 8, 16 and 32.

So, the answer would be 2, 4, 8.

#### Find a number that is a multiple of both 5 and 8.

5 x 8 = 40
Thus, 40 is a multiple of both 5 and 8.

#### A multiple of a number can be equal to the number itself. (True / False)

True.
For example,
21 is a multiple of 1, 3, 7 and 21.
Thus, 21 is a multiple of itself also.

#### Every number is not a multiple of 1. (True / False)

False.
Every number is a multiple of 1.

## 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

#### Each prime numbers has exactly three factors. (True / False)

False.
Each prime numbers has exactly two factors, 1 and the number itself.

#### Which number is neither prime nor composite?

1.
The number 1 is neither prime nor composite.

97

#### Among 13, 15, 21, 23, 27 and 31 which are prime numbers.

13, 23 and 31 are prime  numbers as they have only two factors, 1 and the number itself.

#### Among 9, 18, 20, 23, 30 and 36 which are composite numbers.

Except 23 all other numbers are composite numbers.
23 is a prime number.

## 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.

1. Nice