Factor Definition
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
First, we have to consider the number for which we have to find the factors. Here we are finding the factors of 75.
Then we find those pairs which on multiplication gives us the number 75.
So \[1 \times 75 = 75\] therefore 1 and 75 will be the factors of 75.
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 criteria 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.
FAQs on Factors of 75
1.How to calculate the factor of 75 by factorization method?
Steps to find factors of 75 by factorization method,
First, write the value 75.
Find the 2 numbers, which provides the result as 75 under the multiplication, say 3 and 25, like \[3 \times 25 = 75\].
We know that 3 is the prime which has only two factors that are 1 and 3. So, it cannot be further factorized.
Now we will consider 25 which is a composite number and it can be factored further,
\[25 = 5 \times 5 \times 1\]
Therefore, the factorization of 75 is expressed as \[75 = 3 \times 5 \times 5 \times 1\].
It can also be written as 31 and 52
Finally, write down all the unique numbers which we will obtain from \[3 \times 5 \times 5 \times 1\].
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.
First, we will divide 75 by 1 so it gives us the whole number, therefore (1, 75) are the factors of 75.
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.
It is divisible by 3 because by adding 7 and 5 we are getting 12 which is divisible by 3.
It is not divisible by 4 because on dividing we are getting a decimal number which cannot be the factor.
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.
Similarly, we will continue the procedure and check the divisibility till 10.
After all these steps we will get the factors of 75.
3. What is the method to calculate the Factor of 75?
A number's factors can be determined in a variety of ways, one of which includes dividing the number by the smallest of the factors. The factors of number 75 may be calculated as follows:
Step1: Write down the lowest factor of 75(except 1). Three is the lowest factor of 75.
Step 2: Multiply 75 by 3, or \[\frac{75}{3} = 25\]. As a result, the factors of 75 are 3 and 25.
Step 3: Write the smallest factor of 75 after that. The smallest factor of 75 after that is 5. 75 divided by 5 equals 15. As a result, the factors of 75 are 5 and 15.
Step 4: When writing all of the elements, including 1 and the number itself.
Thus, the factors of 75 are 1, 3, 5, 15, 25, and 75.
4. How to calculate Prime Factorization of 75 by Upside-Down Method?
One of the strategies used in the Prime factorization method to determine factors of integers is Upside-Down Division. In this process, you divide a given "composite" number equally by a series of prime numbers (beginning with the smallest) until you get a prime number. Because the symbol is inverted upside down, it is known as Upside-Down Division. On the RHS, we draw a rectangular line and write the number. Then we try to find a prime number that divides the right-hand number. When we find a prime number like this, we write it on the left. We divide and write the result under the number on the RHS, then we repeat the method until we reach 1. The prime factors are represented by the numbers on the left side. By multiplying those prime numbers, we can find the prime factorization.
5. How can we download study material from Vedantu for important concepts of Mathematics?
Vedantu is a one-stop destination where students may receive all of their free math and other subject’s resources. When it comes to obtaining the most genuine and up-to-date study material, it is a well-known brand. Students just need to go on the Vedantu’s platform and click in the Study Material menu. There, they will get all the subjects and study material details. They just need to click on the specific subject and download the PDF by clicking on it. Regular tests and revision materials can help you score higher on the main exam. Students are allowed to ask questions during a live session, and our mentors are delighted to assist in any situation. Thousands of students have enlisted with us here at Vedantu and are enjoying their effective learning at a time when offline classroom sessions have become a faraway reality owing to the continuing Coronavirus outbreak.
