Factors of 75 | division & prime factorization, Easy Way

factor of 75

The factors of 75 are the numbers that produce 75 when you multiply two numbers together.

 There are no fractions or decimal numbers in the pair factors of 75, so they can either be positive or negative. We will use the division method and the factorization method to find the factors of a number, 75.

 Using the factorization method, first consider the numbers, 1 and 75, then continue finding the other pair of numbers, which will result in 75. For a better understanding of this method, read the article below to calculate the factor 75 in pairs. Here we also discuss the prime factors of 75 using the division method.

factors of 75

What are the Factors of 75?

Basically, the factors of 75 are the numbers multiplied in pairs resulting in the original number 75. Therefore, the factors of 75 are the numbers that divide 75 exactly without leaving a remainder.

Due to the fact that the number 75 is a composite number, it consists of more than just one factor.  As a result, the factors of 75 are :

1, 3, 5, 15, 25, and 75.

What are the Factors of Negative 75?

When we multiply two numbers and get -75 as a product, those numbers are the factors of -75. 

Here is the explanation:

-1 × 75 = -75

  1 × 75 = -75

-3 ×  75 = -75

  3 × -75 = -75

-5 ×  15 = -75

5 ×  -15 = -75

-25 ×  3 = -75

25 ×  -3 = -75

-15 ×  5 = -75

 15 ×  5 = -75

We can get -75 by having (-1, 75), (-3, 25), (-5, 15), (-15, 5), and (-25, 3) as a pair of factors. Similarly, we can also get -75 by having (1, -75), (3, -25), (5, -15), (15, -5), and (25, -3)as a pair of factors.

Pair Factors of 75

In order to find the pair factors, multiply two numbers in a pair by 75 to get the original number. The factors are as follows.

1 × 75 = 75, (1, 75).

3 × 25 = 75, (3, 25)

5 × 15 = 75, (5, 15)

25 × 3 = 75, (25, 3) 

15 × 5 = 75, (15, 5) 

In this case (25, 3) = (25, 3) and (5, 15) = (15, 5)

As a result, the positive pair factors of 75 are (1, 75), (3, 25), and (5, 15).

You can find the negative pair factors by following these steps

-1 × -75 = 75, (-1,- 75) 

-3 × -25 = 75, (-3, -25) 

-5 × -15 = 75, (-5, -15)

-25 × -3 = 75, (-25, -3) 

-15 × -5 = 75, (-15, -5) 

In this case, (-3, -25) is (-25, -3), and (-5, -15) is (-15, -5).

Hence, the negative pair factors of 75 are (-1, -75), (-3, -25), and (-5, -15).

How to calculate the Prime Factors of 75?

You can calculate the factors of a number by following the steps below.

  • Write the number 75 first
  • Find the two numbers that give the same result as 75 when multiplied together, 

such as,

3 × 25 = 75.

  • As we know, 3 is a prime number with only two factors, 1 and itself ( 1 and 3). Therefore, it cannot be further factorized.

3 = 3 × 1

  • However, the number 25 is a composite number and not a prime number. As such, it can be further factored.

25 = 5 × 5 × 1

  • Thus, the factorization of the number 75 is written as follows: 

75 = 3 × 5 × 5 × 1

  • Then, write down all of the unique numbers (i.e.,) 

3 ×  5 × 5 × 1.

Prime Factorization of 75

There should be prime factors in the number 75 since it is a composite number. 

ECTI Pakistan - Factors of 75 by prime factorization

Let’s find out how to calculate the prime factors.

Step 01:

The first thing to do is to divide 75 by the smallest prime factor, say 2. When we divide 75/2, we will get a fractional value, so we will proceed to the next prime factor, (i.e.,) 3.

75 ÷ 3 = 25

Step 02:

When we divide 25 by 3, we get a fractional number, which is not a factor.

Step 03:

Let’s move on to the next prime number, which is.

 25 ÷ 5 = 5

 5 ÷ 5 = 1

As a result of the division process, we received number 1. Therefore, we cannot proceed. As a result, the prime factors of 75 are written as 3 × 5 × 5, or 3 × 52.

Links Related to Factors
Factors of 15= 1, 3, 5, and 15.Factors of 36= 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 48=  1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.Factors of 18= 1, 2, 3, 6, 9 and 18.
Factors of 24=  1, 2, 3, 4, 6, 8, 12, and 24.Factors of 25=  1, 5, and 25.
Factors of 42= 1, 2, 3, 6, 7, 14, 21, and 42.Factors of 60=  1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 35= 1, 5, 7, and 35.Factors of 81= 1, 3, 9, 27, and 81.
Factors of 84=  1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.Factors of 56= 1, 2, 4, 7, 8, 14, 28 and 56.

Solved Examples

Example 1:

Calculate the common factor of 75 and 73.

Solution:

75 has the following factors:

 1, 3, 5, 15, 25 and 75. 

73 has two factors: 

1 and 73

Therefore, the common factor of 75 and 73 is 1.

Example 2:

Determine the common factor of 75 and 76.

Solution:

Factors of 75 = 1, 3, 5, 15, 25 and 75.

Factors of 76 = 1, 2, 4, 19, 38, and 76.

As a result, the common factor between 75 and 76 is 1.

Example 3:

Calculate the common factor of 75 and 150.

Solution:

Factors of 75 = 1, 3, 5, 15, 25 and 75.

Factors of 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

Thus, the common factors of 75 and 150 are 1, 3, 5, 15, 25, and 75.

FAQ`s

What are the factors of 75?

Factors of 75= 1, 3, 5, 15, 25 and 75.

What is the prime factorization of 75?

Prime factorization of 75 = 3 × 5 × 5 or 3 x 52.

What are the positive pair factors of 75?

Positive pair factors of 75= (1, 75), (3, 25), and (5, 15).

What are the negative pair factors of 75?

Negative pair factors of 75= (-1, -75), (-3, -25), and (-5, -15).

Is 25 a factor of 75?

It is true that 25 is a factor of 75. As 25 divides 75 exactly without leaving any remainder, it is a factor of 75.