**Write all the Factors of 48 and How to Find the Pair Factors of 48?**

Here we will learn the Definition of factor, Pair Factors of 48, Prime Factorization, Prime Factorization of 48, List the Factors of 48, List of all positive factors Pairs of 48, and List of all negative factors Pairs of 48 with solved examples.

**Factors of 48**

A number’s factors are the products of numbers that absolutely divide the given number. The number’s factors can be both, either negative or positive. By multiplying a number’s variables, we can obtain any given number. Consider an example 1, 2, 3, 6, these are the factors of 6. We two or more numbers are multiplied; we get the result as 6. Therefore, 2 x 3 = 6 or 1 x 6 = 6. In this topic, we will thoroughly discuss “the factors of 48”.

**What are the factors?**

The numbers multiplied to obtain another number are known as factors. Many numbers are there having more than one factorization such that they can be factored in more than one way. For e.g., the number 12 can be factored as 1 x 12 =12 or 2 x 6 or 3 x 4 = 12

Now, what a prime factor actually is!

A number that can only be factored as 1 time is known as a prime number.

**Factors of 48: Definition**

According to the factors definition, when the numbers are multiplied together, give the original number. For e.g., by multiplying two factors together, we get the original number. Any number’s factors can be either positive or negative integers.

All the **integers** that can evenly divide the given number 48 are the factors of 48.

**How to find the Factors of 48?**

According to the definition of factors, it is understood that all factors of 48 are all positive or negative integers, such that the number 48 can be divided completely.

Now, simply divide the number 48 by every number which completely divides 48 in ascending order till 48.

48 divided by 1:

48 divided by 2:

48 divided by 3:

48 divided by 4:

48 divided by 6:

48 divided by 8:

48 divided by 12:

48 divided by 16:

48 divided by 24:

48 divided by 48:

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

We also know that

48 also have negative factors.

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

**What is Prime Factorization of 48 (Factors of 48)?**

1 multiplied by 48:

1 x 48 = 48

2 multiplied by 24:

2 x 24 = 48

3 multiplied by 16:

3 x 16 = 48

4 multiplied by 12:

4 x 12 = 48

6 multiplied by 8:

6 x 8 = 48

**List the Factors of 48**

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 |

Thus, 48 have 10 positives and 10 negative factors.

**Prime Factorization of 48 (Pair Factors of 48)**

Pair factors of 48 are two factor combinations, that when multiplied together, yield 48.

**List of all positive factors Pairs of 48**

1 multiplied by 48: 48

2 multiplied by 24: 48

3 multiplied by 16: 48

4 multiplied by 12: 48

6 multiplied by 8: 48

8 multiplied by 6: 48

12 multiplied by 4: 48

16 multiplied by 3: 48

24 multiplied by 2: 48

48 multiplied by 1: 48

We know that

All the factors of 48 include negative integers also.

**List of all negative factors Pairs of 48**

-1 multiplied by -48: 48

-2 multiplied by -24: 48

-3 multiplied by -16: 48

-4 multiplied by -12: 48

-6 multiplied by -8: 48

-8 multiplied by -6: 48

-12 multiplied by -4: 48

-16 multiplied by -3: 48

-24 multiplied by -2: 48

-48 multiplied by -1: 48

**Prime Factorization of 48**

It is already understood, according to the concept of prime factor, that the prime factor of a number is the product of all prime factors (a number that divides by itself and only one). As a result, we will list the prime factors from the list of factors of 48.

To find the prime factorization of 48, use either prime factorization or a factor tree.

**Sum of all factors of 48**

We have all the factors of 48.

Therefore, the sum of all factors of 48 can be obtained by the addition of prime factors.

Prime factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Thus, 124 is the sum of all factors of 48.

**Prime factor of any Prime Number**

For e.g., let us know the number 41 prime factors.

We can simplify the task by calculating the square root of a given number. If 41 is not a prime number, it is divisible by at least one prime number that is less than or the square root of the number. Now, make a list of all the prime numbers that are less than 6, which are 2, 3, or 5. Since 41 cannot be split equally by 2, 3, or 5. As a result, we can assume that the number 41 is a prime number. Thus, 41 do not have prime factors.

**Some Solved Examples**

**Write down the factors of 48**

Factors of 48 are as follows

48 divided by 1: 48

48 divided by 2: 24

48 divided by 3: 16

48 divided by 4: 12

48 divided by 6: 8

48 divided by 8: 6

48 divided by 12: 4

48 divided by 16: 3

48 divided by 24: 2

48 divided by 48: 1

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

**Write down the factors of 68**

Factors of 68 are as follows

68 divided by 1: 68

68 divided by 2: 34

68 divided by 4: 17

68 divided by 17: 4

68 divided by 34: 2

68 divided by 68: 1

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

**What are the factors of 416?**

- In Mathematics, 416 is a composite number
- 2 x 2 x 2 x 2 x 2 x 13 represents the prime factorization of 416
- The other way to write the prime factorization(2)
^{5}x 13 - 1, 2, 4, 8, 16, 26, 32, 52, 104, 208, and 416 are the factors of 416.

**What are the Prime Factors of 41?**

We can simplify the task by calculating the square root of a given number. If 41 is not a prime number, it is divisible by at least one prime number that is less than or the square root of the number. Now, make a list of all the prime numbers that are less than 6, which are 2, 3, or 5. Since 41 cannot be split equally by 2, 3, or 5. As a result, we can assume that the number 41 is a prime number. Thus, 41 do not have prime factors.

At Takshila learning factorization and every other numerical concept becomes very easy and simple to understand. By following the solved examples the aspirants can easily solve the problems related to factorization and also can find the prime factors of a number.

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