[Maths Class Notes] on Factors of 48 Pdf for Exam

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get any given number. Let’s take an example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. In this session we will study the factors of 36 definitions, how to find the factors of 36 and examples. Let’s discuss the factors of 48.

What are Factors?

Factors can be defined as the numbers you multiply to get another number. There are many numbers that have more than one factorization (it means that they can be factored in more than one way). For instance, the number 12 can be factored as 1×12 or 2×6 or 3×4. Here’s what a prime factor is!A number that can only be factored as 1 times it is known as a prime number.Factors of 48 DefinitionThe factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors of any number can be either positive or negative integers.Factors of 48 are all the integers that can evenly divide the given number 48.Now let us find all factors of 48.

How to Find the Factors of 48(Prime Factorization of 48)?

According to the definition of factors of 48 we know that all factors of 48 are all the positive or negative integers which divide the number 48 completely. So let us simply divide the number 48 by every number which completely divides 48 in ascending order till 48.

48 ÷ 1 = 48 

48 ÷ 2 = 24 

48 ÷ 3 = 16 

48 ÷ 4 = 12

48 ÷ 6 = 8

48 ÷ 8 = 6

48 ÷ 12= 4

48 ÷ 16 = 3

48 ÷ 24 = 2

48 ÷ 48 = 1

So the factors of 48-1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

We know that factors also include negative integers hence we can also have, list of negative factors of 48 are -1,-2,-3,-4,-6,-8,-12,-16,-24 and -48.

What are the Factors of 48 (Prime Factorization of 48)?1 x 48 = 48, 2  x 24 = 48, 3  x 16 = 48, 4  x 12 = 48, 6  x 8 = 48 Factors of 48 can be Listed as Follows. Positive 

Factors of 48 

1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Negative Factors of 48-1,-2,-3,-4,-6,-8,-12,-16,-24 and -48

Hence 48 have a total 10 positive factors and 10 negative factors.

Pair Factors of 48 (Prime Factorization of 48)

Let’s know the pair factors of 48.

Factor Pairs of 48 are combinations of two factors that when multiplied together give 48.

List of all the Positive Factor Pairs of 48

1 x 48 = 48

2 x 24 = 48

3 x16 = 48

4 x 12 = 48 

6 x 8 = 48 

8 x 6 = 48 

12x 4 = 48 

16 x 3 = 48 

24 x 2 = 48 

48 x 1 = 48 

As we know that all Factors of 48 include negative integers too. List of all the Negative Factor Pairs of 48:

-1 x -48 = 48

-2 x -24 = 48

-3 x-16 = 48

-4 x -12 = 48 

-6 x- 8 = 48 

-8 x- 6 = 48 

-12x- 4 = 48 

-16 x- 3 = 48 

-24 x- 2 = 48 

-48 x -1 = 48 

Factors Of 48 

To determine the factor of 48, we first have to check whether it is a prime number or a composite number. The number 48 comes out to be a composite number as it has more than two factors ( 1 and 48 itself). Therefore, we have to now find all its factors which come out to be 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. If you check, you will see that the number 48 is divisible by all these numbers. 

Examples for Finding Factors of Other Numbers

Solution: The number 20 is divisible by 1, 2, 4, 5, 10 and 20. So, these six numbers are its factors 

Solution: We can see that the number 36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18 and 36. Therefore, all these numbers are factors of 36.

What is Prime Factorization? 

When you express a number in terms of the product of its prime factors, then it is called prime factorization. For example, if we again take the example of the number 48 and express it as 2×2×2×2×3, then this product of its prime factors (2 and 3) can be called its prime factorization. Now let’s solve some examples so that you can grasp them completely. 

Solution: 30 in terms of its prime factorisation can be written as 2×3×5. Here, we can see that the prime factors of the number 30 are 2, 3 and 5.

Solution: The prime factorisation of the number 72 is 2×2×2×3×3 with 2 and 3 being the prime factors of 72.

Solution: The number 130 can be written as 2×5×13 which will be its prime factorisation. Here, the numbers 2, 5 and 13 are the prime factors of 130. 

So, this was all about Factors of 48, its prime factorisation, etc. We have provided enough examples to let you understand this topic. If you are still not able to understand this topic, you can refer to online video lectures for Maths or Maths NCERT books which will help you to understand this properly. You can find both of these resources on the website or the app. 

Prime Factorization of 48

According to the prime factor definition we know that the prime factor of a number is the product of all the factors that are prime ( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 48.Or the other way to find the prime factorization of 48 is by prime factorization or by factor tree. We know all the factors of 48, so the sum of all factors of 48 is –Prime factors -1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Therefore, the sum of all factors of 48 is 124. Prime Factor of any Prime Number:For example let’s find the prime factor of 41:To make the task easier we can find the square root of the given number. Let’s suppose that 41 is not a prime number, then the number would be divisible by at least one prime number which is less than or equal to the square root of the number √41 ≈ 6.4. Now, list all the prime numbers less than 6 which are 2,3 and 5 and since 41 cannot be divided evenly by 2, 3, or 5, we can conclude that 41 is a prime number. So there are no prime factors of 41.

Solved Examples

Example 1: Write down the factors of 48.

Solution) 48 ÷ 1 = 48

48 ÷ 2 = 24

48 ÷ 3 = 16

48 ÷ 4 = 12

48 ÷ 6 = 8

48 ÷ 8 = 6

48 ÷ 12= 4

48 ÷ 16 = 3

48 ÷ 24 = 2

48 ÷ 48 = 1

Therefore the factors of 16 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Example 2: Write down the factors of 68.

Solution: 68 ÷ 1 = 68

68 ÷ 2 = 34

68 ÷ 4 = 17

68 ÷ 17 = 4

68 ÷ 34 = 2

68 ÷ 68 = 1

Therefore the factors of 16 are 1, 2, 4, 17, 34 and 68.