## Factors and Multiples

#### What are factors?

Set of whole numbers when multiplied gives a product. Those whole numbers are called factors of the product.

6 is also a factor of 30 since 6 × 5 = 30

**Example 1:**3 × 5 = 15. 3 and 5 are factors of 15.**Example 2:**2 × 3 × 5 = 30. 2, 3 and 5 are factors of 30.6 is also a factor of 30 since 6 × 5 = 30

#### What are multiples?

Product of one number multiplied by another number

2, 4, 6, 8, 10 are multipes of 2.

**Example 1:**2 × 1 =**2**, 2 × 2 =**4**, 2 × 3 =**6**, 2 × 4 =**8**, 2 × 5 =**10**2, 4, 6, 8, 10 are multipes of 2.

#### What is Greatest Common Divisor (GCD) or Greatest Common Factor (GCF)?

The greatest common divisor (GCD or GCF) of two numbers is the greatest number that divides both the numbers.

For e.g.: The factors of 6 are: 1, 2 and 3.

The factors of 8 are: 1, 2 and 4

The greatest number that divides both 6 and 8 is 2. Hence

For e.g.: The factors of 6 are: 1, 2 and 3.

The factors of 8 are: 1, 2 and 4

The greatest number that divides both 6 and 8 is 2. Hence

**2 is the GCD of 6 and 8**.#### What is Least Common Multiple (LCM)?

The least common multiple (LCM) of two numbers is the smallest number that is divisible by both the numbers.

For e.g.: The multiples of 2 are: 2, 4, 5, 8, 10.

The multiple of 3 are: 3, 6, 9, 12, 15

The smallest number that is divisible by both 2 and 3 is 6. Hence,

For e.g.: The multiples of 2 are: 2, 4, 5, 8, 10.

The multiple of 3 are: 3, 6, 9, 12, 15

The smallest number that is divisible by both 2 and 3 is 6. Hence,

**6 is LCM of 2 and 3.**#### 1. Find the factors of 8.

1 × 8 = 8

8 is the

So 1 and 8 are

2 × 4 = 8

8 is the

So, 2 and 4 are

The factors of 8 are 1, 2, 4 and 8.

8 is the

**product**of 1 and 8.So 1 and 8 are

**factors**of 8.2 × 4 = 8

8 is the

**product**of 2 and 4.So, 2 and 4 are

**factors**of 8.The factors of 8 are 1, 2, 4 and 8.

1 is a factor of every number.

Every number is a factor of itself.

Every number is a factor of itself.

#### 2. Find the multiples of 8.

To find the multiple of 8, think of the times table of 8 as below.

8 × 1 = 8, 8 × 2 = 16, 8 × 3 = 24,

8 × 4 = 32, 8 × 5 = 40, 8 × 6 = 48,

8, 16, 24, 32, 40 and 48 are

8 × 1 = 8, 8 × 2 = 16, 8 × 3 = 24,

8 × 4 = 32, 8 × 5 = 40, 8 × 6 = 48,

8, 16, 24, 32, 40 and 48 are

**multiples**of 8.
8 is a factor of all the multiples of 8.

#### 3. List all the factors of 60.

60 = 1 × 60

60 = 2 × 30

60 = 3 × 20

60 = 4 × 15

60 = 5 × 12

60 = 6 × 10

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

60 = 2 × 30

60 = 3 × 20

60 = 4 × 15

60 = 5 × 12

60 = 6 × 10

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

#### 4. What are the common factors of 16 and 24? What is the greatest common factor of 16 and 24?

The factors of 16 are:

The factors of 24 are:

The

The

**1**,**2**,**4**,**8**and 16.The factors of 24 are:

**1**,**2**, 3,**4**, 6,**8**, 12 and 24.The

**common factors**of 16 and 24 are 1, 2, 4 and 8.The

**greatest common factor (GCF)**of 16 and 24 is 8.#### 5. List the first six multiples of 6. What is the twelfth multiple of 6?

6 × 1 =

6 × 4 =

The

The

The

The

The

The

The

**6**, 6 × 2 =**12**, 6 × 3 =**18**,6 × 4 =

**24**, 6 × 5 =**30**, 6 × 6 =**36**,The

**first multiple**of 6 is 6.The

**second multiple**of 6 is 12.The

**third multiple**of 6 is 18.The

**fourth multiple**of 6 is 24.The

**fifth multiple**of 6 is 30.The

**sixth multiple**of 6 is 36.The

**twelfth multiple**of 6 is 6 ×**12**or**72**.#### 7. Is 21 a multiple of 7?

21 can be divided exactly by 7.

21 is a multiple of 7.

7 is a factor of 21.

21 is a multiple of 7.

7 is a factor of 21.

#### 8. Is 25 a multiple of 7?

25 cannot be divided exactly by 7.

25 is

7 is not a factor of 25.

25 is

**not**a multiple of 7.7 is not a factor of 25.

#### 9. Find the first six multiples of 2 and 5. What is a common multiple of 2 and 5?

The first six multiples of 2 are 2, 4, 6, 8,

The first six multiples of 5 are 5,

A

**10**and 12.The first six multiples of 5 are 5,

**10**, 15, 20, 25 and 30.A

**common multiple**of 2 and 5 is**10**.#### 10. I'm thinking of a one-digit number, N, which is greater than 1.

N and 7 are the common factors of 14 and 28.

What is the number I'm thinking of?

The factors of 14 are 1, 2, 7 and 14.

The factors of 28 are 1, 2, 4, 7, 14 and 28.

The common factors of 14 and 28 are 1, 2, 7 and 14.

The one-digit common factor of 14 and 28 other than 1 and 7 is 2.

N is

The factors of 28 are 1, 2, 4, 7, 14 and 28.

The common factors of 14 and 28 are 1, 2, 7 and 14.

The one-digit common factor of 14 and 28 other than 1 and 7 is 2.

N is

**2**.