Concept of factorization

Factorisation is a crucial mathematical topic that finds and defines its real-time utility itself. In simple words, a factor can be termed as a divisor of any number. Any number that can completely divide another number is often called the factor of the latter. The mathematical multiplication concept forms the basis of the Factorisation concept. The main point to be noted is that the factors of a number are always less than or equal to the number itself. The factors can never be greater than the numbers. 

Assessment of factors can be done using either multiplication or addition concepts. Let’s study and take a look at the details of the concept of Factorisation. Application of divisibility principles can perfectly help to solve the factorisation problems without much effort.

Define factors in simple and easy words

Any number dividing the given number completely is called the factor of that number. It may be a number or algebraic expression. For positive numbers, the factors are positive in general but it would be better to know that two negative numbers also become the factors of a positive integer when multiplied together. Just like 6*4 is 24 where 6 & 4 are the factors of 24 but if (-6) is multiplied with (-4) then also the product is 24 which means that (-6) & (-4) are also factors of 24. But often preferences are given to the positive ones. Related to factors is an important topic of multiples. Both of these can be finite in number for a composite number. 

Properties related to Factorisation

Certain important features and properties applicable to the concept of factors define it better. 

  • There can be an endless number of factors for any composite number but for prime numbers the factors only 1 & the number itself.
  • The factors <= the number itself.
  • All numbers can be written as a product of their factors.
  • 0 is not a factor of any number.
  • The basic concept of multiplication and division is utilized for finding factors.

Using multiplication and division for acknowledging the factors of numbers

Through the use of multiplication 

Calculation of factors using this method includes the following steps: 

  • Assess the numbers whose product give the number in every possible way on multiplying.
  • The digits involved in the products are known as the factors for the given number.
  • The easiest way to do so is by beginning from the lowest number and proceeding in ascending order.

The numbers thus obtained would be the factors of the given number.

For example Factors of 25 can be found as

1*25= 25

5*5= 25, so the factors of 25 will be 1, 5, 25.

Similarly, the factors of 32 can be found by the product (multiplication) method as:

1*32 

2*16

4*8

Factors of 32 are 1, 2, 4, 8, 16, 32.

Through the use of division

Calculation of factors using this method includes the following steps: 

  • Assess the numbers that can divide the given number. 
  • Get the quotient by dividing the given number with one that divides it completely.
  • The divisor that leaves the remainder as zero on dividing the original number is the final factor.

For example Factors of 108 can be 

108÷1=108

108÷2=54

108÷3=36

108÷4=27

108÷6=18

108÷9=12

So, factors of 108 are 1,2,3,4,6,9,12,18,27,36,54,108.

Prime factorisation of any number 

The method of prime factorization is also used to find the factors of a given number. The representation of factors, in this case, is in exponential form. The steps included are as follows:

  • Assess the given number as a product of various prime numbers.
  • Represent the number as a product of factors in exponential form.
  • The solution can be verified by finding the product of the factors obtained. The same is equal to the original number. 

The explanation above gives a detailed analysis of the topic factors. Cuemath app explains the concept better with a lot of examples and problems for practice.