 # Factors of 75

## The Factors of 75

The factors of a number 75 are those numbers which on multiplication with each other gives us the number 75. Factors of 75 can be positive numbers or negative numbers.  Factors cannot be fractions or decimal numbers. It is always a whole number only. The factors can also be negative.  Upon multiplication of two negative numbers, we get a positive value. To find the factors of 75 there are many different methods, like factorization, prime factorization, and divisibility methods.

## Here We will Calculate Some Factors of 75 by Using the Division Method.

 75 ÷ 1 = 75 75 ÷ 2 = not divisible 75÷ 3 the = 25 75 ÷ 4 = not divisible 75 ÷ 5 =15 75÷ 6 = not divisible 75 ÷ 7 = not divisible 75 ÷ 8 = not divisible 75 ÷ 9 = not divisible 75 ÷ 10 = not divisible 75 ÷ 11 = not divisible 75÷ 12 = not divisible 75÷ 13 = not divisible 75 ÷ 14 = not divisible 75 ÷ 15 = 5 75÷ 16 = not divisible 75 ÷ 17 = not divisible 75 ÷ 18 = not divisible 75 ÷ 19 = not divisible 75 ÷ 20 = not divisible

Following the multiplication tables up to 20, we can easily find the factors of 75.

### Steps To Find The Pair Factors Of 75:

1. First, we have to consider the number for which we have to find the factors. Here we are finding the factors of 75.

2. Then we find those pairs which on multiplication gives us the number 75.

3. So 1 × 75 = 75  therefore 1 and 75 will be the factors of 75.

4. Similarly, we will find more factors

3 × 25 = 75, (3, 25).

5 × 15 = 75, (5, 15).

25 × 3 = 75, (25, 3).

15 × 5 = 75, (15, 5).

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

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

To find the negative pair factors, we will follow the same steps.

If -1 × -75 = 75, then (-1, - 75) are the factor of 75.

Similarly, -3 × -25 = 75, (-3, -25).

-5 × -15 = 75, (-5, -15).

-25 × -3 = 75, (-25, -3).

-15 × -5 = 75, (-15, -5).

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

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

### Factorization Method To Find The Factors Of 75:

In the factorization method, first consider the numbers, 1 and 75 as the factors of 75, and then continue with finding more pairs of factors that on multiplication gives us the original number.

We consider negative numbers as factors because on multiplying two negative numbers we get a positive value So, it does not make any changes in the number for which we are finding the factors.

Another method to calculate the factor of 75 is by using the divisibility method.

### Prime Factorization Method

In this method, the number 75 is first divided by the smallest prime number that is 2. If it does not divide by 2, we proceed for the next prime number that is 3.

Here 75 can be divided by 3 so we divide it. Further, if it is possible to divide it again by 3 we will divide it. Otherwise, we will proceed to the next prime number.

By this method, we can find the factors of 75.

1.How to calculate the factor of 75 by factorization method?

Answer: Steps to find factors of 75 by factorization method,

1. First, write the value 75.

2. Find the 2 numbers, which provides the result as 75 under the multiplication, say 3 and 25, like 3 × 25 = 75.

3. We know that 3 is the prime which has only two factors that are 1 and 3. So, it cannot be further factorized.

4. Now we will consider 25 which is a composite number and it can be factored further,

25 = 5 × 5 × 1

Therefore, the factorization of 75 is expressed as 75 = 3 × 5 × 5 × 1.

It can also be written as 31 and 52

Finally, write down all the unique numbers which we will obtain from 3 × 5 × 5 × 1.

The factors of 75 can be written as

2. What are the steps to calculate factors of 75 using the divisibility method?

The number 75 is a composite number and it should have prime factors. Use the steps given below to find the factor of 75.

1. First, we will divide 75 by 1 so it gives us the whole number, therefore (1, 75) are the factors of 75.

2. Now checking the visibility of 2 it is not divisible by 2 because it does not have an even number in the unit’s place.

3. It is divisible by 3 because by adding 7 and 5 we are getting 12 which is divisible by 3.

4. It is not divisible by 4 because on dividing we are getting a decimal number which cannot be the factor.

5. It will be divisible by 5 because it has 5 in the unit’s place which is the required condition to check the divisibility of 5.

6. Similarly, we will continue the procedure and check the divisibility till 10.

7. After all these steps we will get the factors of 75.