Factors of 75 | How to Find Them | Easy Way

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 the 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. To better understand 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.

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.

Similarly, if I consider some examples for a better understanding of factors are

Factors of 24

1, 2, 3, 4, 6, 8, 12, and 24.

And Factors of 39

| 1, 3, and 13.

So from the above examples as you can see that the Factors of even numbers will be even and odd factors for an odd number.

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. 

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.

Solved Examples

Example 1:

Calculate the common factor of 75 and the factors of 39.

Solution:

75 has the following factors:

 1, 3, 5, 15, 25 and 75. 

39 has four factors: 

1, 3, 13 and 39.

Therefore, the common factors of 75 and 39 are 1 and 3.

Example 2:

Determine the common factor of 24 and 76.

Solution:

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

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

As a result, the common factor between 24 and 76 are 1, 2, and 4.

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