The factors of NS 75 are the numbers which when two numbers are multiplied together give the result of 75. Pair factors of 75 are whole numbers that can be either positive or negative but not fractions or decimal numbers.

To find the factors of the number, 75, we can use two methods –

- Division method and
- Factorization method.

The factorization method is easy to apply, In this method one must consider the numbers 1 and 75 first, and continue searching for the second pair of numbers, resulting in 75.

To understand this method better, you can find the factor of 75 by reading the article given below. Also, the prime factors of 75 by division method are discussed here.

**Factors of 75 are – **1, 3, 5, 15, 25 and 75.

- Pair Factors of 75: 1×75, 3×35, and 5×15
- Prime Factorization Factors of 75 :- 3×5×5

## What are the factors of 75?

The factors of 75 are the numbers that are multiplied in pairs to get the original number 75. In other words, the factors of 75 are the numbers that exactly divide 75 without leaving any remainder.

The number 75 is composite, it is a factor of many numbers other than the number itself. Given below are the numbers, the factors of 75 are 1, 3, 5, 15, 25 and 75.

## The pair factor

For the pair factor of 75 numbers, multiply two numbers in a pair to get the original number 75. Given below are the factors of 75 numbers.

If 1 × 75 = 75, then (1, 75) is the pair factor of 75.

**Similarly, let us make another pair**

- 3 × 25 = 75, (3, 25) 75 is a pair factor of the number
- 5 × 15 = 75, (5, 15) 75 is a pair factor of the number
- 25 × 3 = 75, (25, 3) 75 is a pair factor of the number
- 15 × 5 = 75, (15, 5) 75 is a pair factor of the number

Here also, (3, 25) is the same (25, 3) and (5, 15) is the same (15, 5). The positive pair factors of 75 numbers are (1, 75), (3, 25), and (5, 15).

**To find the pair factorization of negative numbers, the following are given below.**

- If –1 × –75 = 75, then (–1,– 75) 75 is a pair factor of the numbers
- -3 × -25 = 75, (-3, -25) 75 is a pair factor of the numbers
- -5 × -15 = 75, (-5, -15) 75 is a pair factor of the number
- -25 × -3 = 75, (-25, -3) 75 is a pair factor of the number
- -15 × -5 = 75, (-15, -5) 75 is a pair factor of the number

Here also, (-3, -25) is the same as (-25, -3) and (-5, -15) is the same as (-15, -5)

The negative pair factors of 75 numbers are (-1, -75), (-3, -25), and (-5, – 15)

## How to calculate prime factors of 75?

** Below are the following steps to calculate the factors of a number.**

- First, write the number of 75.
- Find two numbers that, under multiplication, give a result of 75, say 3 and 25, such that 3 × 25 = 75.
- We know that 3 is a prime number that has only two factors, i.e., 1 and the numbers themselves (1 and 3). Therefore, it cannot be further factored in.
- 3 = 3 × 1
- However, if you look at the number 25, it seems to be a composite number but not a prime number. So it can be further factored in.
- 25 = 5 × 5 × 1
- Therefore, the factorization of 75 is written as 75 = 3 × 5 × 5 × 1
- Finally, write down all the unique numbers (that is,) 3 × 5 × 5 × 1.

## Prime factorization of 75

The number 75 is a composite and must have prime factors. Let us now know how to calculate the factors of prime numbers.

- If 75 is to be divided by the smallest prime factor, let’s say 2. You divide 75/2, you will get a fractional value, and so proceed with the next prime factor, (ie) 3. 75/3 = 25

- Now, if you divide 25 by 3, you will get a fractional number which cannot be a factor.

- So, now you proceed with the next prime numbers, i.e.
- 25/5 = 5
- 5/5 = 1

Lastly, you got the number 1 at the end of the segmentation process. So that we cannot move forward. The prime factors are written as 3 × 5 × 1 or 3 x 5, where 3 and 5 are prime numbers.