In math, a Factor is a number or algebraic expression that is an exact divisor with no remainder. An integer that has the factors one and itself is known as prime factors. The integer that has more than two factors is known as composite factors. Let us learn more about the factors from this article. Go through the below section to know how to find the factors of the numbers from here.

Do refer:

## Factor – Definition

A factor is derived from the Latin word which means “a maker” or “a doer” or “a performer”. A factor is a whole number that can be multiplied by another whole number to produce a whole number.

Factor × Factor = Multiple

### Types of Factors

There are two types of factors. They are

1. Prime factors

2. Composite Factors

**Prime Factors**

Prime factors of a number are the set of prime numbers which when multiplied by together give the actual number. The prime numbers are 2, 3, 5, 7, 11, 13, 17,….

**Example:**

Write the prime factors for 6.

**Solution:**

1 × 6 = 6

2 × 3 = 6

3 × 2 = 6

6 × 1 = 6

2 and 3 are the prime numbers.

Hence, 2 and 3 are the prime factors of 6.

**Composite Factors**

Composite factors of a number are the factors that are not prime. That means the numbers which have more than two factors are known as the composite factors.

**Example:**

Write the composite factors of 12.

**Solution:**

1 × 12 = 12

2 × 6 = 12

3 × 4 = 12

4 × 3 = 12

6 × 2 = 12

12 × 1 = 12

Thus the factors of 12 are 1, 2, 3, 4, 6, 12.

### How to Find Factors of a Number?

We can find the factors of a number by using both the division method and the multiplication method. First, we will see how to find the factors of a number by division.

**Factors by Division**

1. Find the numbers less than or equal to the given number.

2. Now divide the given number by each of the numbers.

3. The remainder should be 0.

For example, let us divide 6 and 3

6 ÷ 3 = 2

Thus the factors of 6 are 2 and 3 as the remainder leaves zero.

**Factors by Multiplication**

Follow the below steps to find the factors using the multiplication method.

1. First write the given numbers as the product of two numbers in possible ways.

2. All the numbers involved in all these products are the factors of the given number.

3. With this we can find whether the given number is a prime factor or composite factor.

For example, write the factors of 12.

1 × 12 = 12

2 × 6 = 12

3 × 4 = 12

4 × 3 = 12

6 × 2 = 12

12 × 1 = 12

Thus the factors of 12 are 1, 2, 3, 4, 6 and 12.

### Solved Problems on Finding Factors

**Example 1.**

Find the factors of 16.

**Solution:**

The factors of 16 are as follows

1 × 16

2 × 8

4 × 4

8 × 2

16 × 1

Therefore the factors of 16 are 1, 2, 4, 8, 16.

**Example 2.**

Write the prime factors for 15.

**Solution:**

Prime factors of a number are the set of prime numbers which when multiplied by together give the actual number.

We have to multiply directly with the prime number to find the factors of 15.

15 = 3 × 5

Thus the prime factors of 15 are 3, 5.

**Example 3.**

Find the Missing Factors of the following

i. 2 × _ = 10

ii. _ × 7 = 21

iii. 7 × _ = 49

iv. 9 × _ = 54

v. 10 × _ = 30

**Solution:**

i. 2 × _ = 10

Let the missing factor be x.

2 × x = 10

x = 10 ÷ 2

x = 5

Thus the missing factor is 5.

ii. _ × 7 = 21

Let the missing factor be a.

a × 7 = 21

a = 21 ÷ 7

a = 3

Thus the missing factor is 3.

iii. 7 × _ = 49

Let the missing factor be b.

7 × b = 49

b = 49 ÷ 7

b = 7

Thus the missing factor is 7.

iv. 9 × _ = 54

Let the missing factor be c.

9 × c = 54

c = 54 ÷ 9

c = 6

Thus the missing factor is 6.

v. 10 × _ = 30

Let the missing factor be y.

10 × y = 30

y = 30 ÷ 10

y = 3

Thus the missing factor is 3.

**Example 4.**

What are the factors of 72?

**Solution:**

The factors of 72 are

1 × 72

2 × 36

3 × 24

4 × 18

6 × 12

8 × 9

9 × 8

12 × 6

18 × 4

24 × 3

36 × 2

72 × 1

Therefore the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

**Example 5.**

What are the factors of 120?

**Solution:**

The factors of 120 are

1 × 120

2 × 60

3 × 40

4 × 30

5 × 24

6 × 20

8 × 15

10 × 12

12 × 10

15 × 8

20 × 6

24 × 5

30 × 4

40 × 3

60 × 2

120 × 1

Therefore the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30, 40, 60 and 120

**Example 6.**

Write the common factors of 21.

**Solution:**

Multiples of 3 – 3, 6, 9, 12, 15, 18, 21, 24.

Multiples of 7 – 7, 14, 21, 28.

Thus the common factors of 21 are 3 and 7.

### FAQs on Factors

**1. Define Factor**

Factors are the numbers you multiply together to get another number. The factor may be both positive integer and negative integer.

**2. What are the factors of 18?**

The factors of 18 are

1 × 18

2 × 9

3 × 6

6 × 3

9 × 2

18 × 1

Thus the factor of 18 is 1, 2, 3, 6, 9, 18.

**3. What are the types of factors?**

There are three types of factors. They are

1. Direct

2. Distributed

3. Augmentative