[Maths Class Notes] on Factors of 75 Pdf for Exam

Factors are defined as the number multiplied by another number to obtain the original numbers. A factor of a number may alternatively be described as an algebraic statement that evenly divides any given integer with a zero remainder. To put it another way, it’s also known as the sum of numerous components. A number’s factors might be either positive or negative. To study about the Factors in detail, click here.

Properties of Factors

A number’s factors have a variety of characteristics. The qualities of factors are listed below:

• A number has a finite number of components.

• A number’s factor is always less than or equal to the provided number.

• Except for 0 and 1, every number has at least two factors: 1 and itself.

• The processes needed to find the factors are division and multiplication.

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

 

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 times 75 = 75] therefore 1 and 75 will be the factors of 75.

4. Similarly, we will find more factors

[3 times 25 = 75, (3, 25).]

[5 × 15 times 75, (5, 15).]

            [25 × 3 times 75, (25, 3).]

            [15 × 5 times 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 times -75 = 75], then (-1, – 75) is the factor of 75.

Similarly, [-3 times -25 = 75, (-3, -25).]

                 [-5 times -15 = 75, (-5, -15).]

                [ -25 times -3 = 75, (-25, -3).]

                [ -15 times -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 by 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.

 

factors of 75, properties of factors, steps to find the pair factors of 75, factorization method to find the factors of 75.

 

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.

 

Definition of Divisibility Test

A divisibility test is a quick way to see if a given number is divisible by a defined divisor without having to divide it, usually by looking at its digits. A number is said to be divisible by another number if the output of the division is a whole number. If the result of dividing a number by another number is a whole number, we say that number is divisible. Because no number is entirely divisible by every number, such numbers have a remainder other than zero. Nonetheless, some crite
ria allow us to discover the true divisor of a number just by looking at its digits.

 

Important Notes from the Chapter

• A number’s prime factors are not the same as its factors.

• The number n is a perfect square if it has an odd number of positive elements.

• A composite number is one that contains more than two components.

• The factors of any number are 1 and the number itself.

• Between[(n, frac{n}{2})] there are no factors of the integer n.

• The smallest prime number is 2; 1 is not a prime number.

• The procedures used in determining the factors are division and multiplication.