 # Factors of 75

The factors of 75 are the numbers, that produce the result as 75 when two numbers are multiplied together. Pair factors of 75 are the whole numbers which could be either positive or negative but not a fraction or decimal number.  To find the factors of a number, 75, we will use the factorization method. In the factorization method, first consider the numbers, 1 and 75, and continue with finding the other pair of multiples of 75 which gives the results as an original number. To understand this method in a better way, read the below article to find the factor 75 in pairs. Also, the prime factors of 75 with the help of the division method is discussed here

## Pair Factors of 75

To find the pair factors, multiply the two numbers in a pair to get the original number as 75, such numbers are as follows

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

Similarly, let us find another pair.

3 × 25 = 75, (3, 25) is a pair factor of 75

5 × 15 = 75, (5, 15) is a pair factor of 75

25 × 3 = 75, (25, 3) is a pair factor of 75

15 × 5 = 75, (15, 5) is a pair factor of 75

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

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

To find the negative pair factors, then proceed with the following steps

If -1 × -75 = 75, then (-1,- 75) is a pair factor of 75

-3 × -25 = 75, (-3, -25) is a pair factor of 75

-5 × -15 = 75, (-5, -15) is a pair factor of 75

-25 × -3 = 75, (-25, -3) is a pair factor of 75

-15 × -5 = 75, (-15, -5) is a pair factor of 75

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

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

## How to calculate the Factors of 75?

Learn the following steps to calculate the factors of a number.

• First, write the number 75
• Find the two numbers, which gives the result as 75 under the multiplication, say 3 and 25, such as 3 × 25 = 75.
• We know that 3 is a prime number which has only two factors, i.e., 1 and the number itself( 1 and 3). So, it cannot be further factorized.
• 3 = 3 × 1
• But look at the number 25, which is a composite number but not a prime number. So it can be further factorized.
• 25 = 5 × 5 × 1
• Therefore, the factorization of 75 is written as, 75 = 3 × 5 × 5 × 1
• Finally, write down all the unique numbers which we can obtain from 3 ×  5 × 5 × 1.
 Factors of 75 1, 3, 5, 15, 25 and 75

### Prime Factors of 75 By Division Method

The number 75 is a composite and it should have prime factors. Now let us know how to calculate the prime factors.

• The first step is to divide the number 75 with the smallest prime factor, say 3.
• 75 ÷ 3 = 25
• Now, if we divide 25 by 3 we will get a fractional number, which cannot be a factor.
• So, now proceed with the next prime numbers, i.e.

25 ÷ 5 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 75 are written as 3 × 5 × 5 or 3 x 52, where 3 and 5 are the prime numbers.

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