Factors

Factors

As we know, every factor of a number is an exact divisor of that number. Factors are the numbers you multiply together to get another number. The process of finding the factors for a given number is better understood by making suitable arrangements. For example, to find the factors of 2, we have to arrange two objects in different ways. These arrangements are useful for writing the factors of a number. The below figure shows the factors of 2.

Factors of 2

Now, let’s find the factors of the smallest composite number, i.e. 4. Here, 4 objects are arranged in 3 different ways. Based on these arrangements, factor pairs and the factors of 4 are given.

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Factors of 4

In the above figure, 4 objects are arranged in 3 ways, i.e.

  • One column with 4 objects
  • 2 rows and 2 columns (that means two rows/column with 2 objects each)
  • One row with 4 objects

Thus, factor pairs are (1, 4), (2, 2) and (4, 1).

Factors are 1, 2, and 4.

Similarly, we can find the factors of 6. This can be observed from the following figure.

Factors of 6

In the above example, the factors of 6 are expressed in a different way. Arrangements are given for visualisation, whereas the division of numbers has been given for the purpose of providing you with another way of getting the factors for a given number.

Therefore, the factors of 6 are 1, 2, 3, and 6.

Some of the important facts about factors of a number are listed below:

  • 1 is a factor of every number
  • Every number is a factor of itself
  • Every factor is less than or equal to the given number
  • The number of factors of a given number are finite

Now, one may get questions on how many factors a number has and how to find these factors. In this section, you will understand the process of finding factors of a given number clearly.

Factors of 36

We can find the factors of 36 as given below:

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

Now we have got the repeated numbers in the multiplication. Hence, we should stop writing 36 as the product of other numbers.

Thus, the factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 24

Let’s write the number 24 as the product of numbers.

1 × 24 = 24

2 × 12 = 24

3 × 8 = 24

4 × 6 = 24

6 × 4 = 24

Now, there is a repeated multiplication so we have to stop the multiplication.

Hence, the factors of 24 are: 1, 2, 3, 4, 6, 12 and 24

Factors of 72

Representation 72 as the product of other numbers is given as:

1 × 72 = 72

2 × 36 = 72

3 × 24 = 72

4 × 18 = 72

6 × 12 = 72

8 × 9 = 72

9 × 8 = 72

Now, we have repeated multiplication so we have to stop the multiplication.

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

Factors of 12

Finding the factors of 12 is simple as given below:

1 × 12 = 12

2 × 6 = 12

3 × 4 = 12

4 × 3 = 12

Therefore, the factors of 12 are: 1, 2, 3, 4, 6 and 12

A number for which the sum of all its factors is equal to twice the number is called a perfect number. From this definition, we can say that the numbers 6 and 28 are perfect. This can be proved as given below:

As mentioned above, the factors of 6 are 1, 2, 3 and 6.

Now, we have to find the factors of 28.

1 × 28 = 28

2 × 14 = 28

4 × 7 = 28

7 × 4 = 28

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

Let’s add the factors of these numbers.

Sum of the factors of 6:

1 + 2 + 3 + 6 = 12 = 2 × 6 (that means twice the number)

Sum of the factors of 28:

1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28 (that means twice the number)

Therefore, 6 and 28 are perfect numbers.

The below table shows the list of factors of numbers. This will help you in solving the problems involving factors, common factors and prime factors in maths.

Factors of Numbers

factors of 10

factors of 120

factors of 18

factors of 25

factors of 98

factors of 415

factors of 80

factors of 4

factors of 70

factors of 30

factors of 68

factors of 23

factors of 63

factors of 216

factors of 6

factors of 215

factors of 49

factors of 17

factors of 105

factors of 150

factors of 101

factors of 108

Frequently Asked Questions on Factors

What are the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6 and 12. These can be represented using multiplication as: 1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12.

How do you explain factors?

Factors can be defined as the exact divisors of a given number. Also, factors are the numbers that are multiplied together (suitable combinations) to produce the original number.

What are factors of 16?

The factors of 16 are: 1, 2, 4, 8 and 16. The factors of 16 can be expressed in terms of multiplication of numbers as given below:
1 × 16 = 16
2 × 8 = 16
4 × 4 = 16

What are the factors for 42?

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21 and 42

What are factors of 90?

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

What are factors of 81?

The factors of 81 are: 1, 3, 9, 27 and 81

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