Mathematics is not a narrow subject its diversity is huge and it covers the most critical subjects of calculation including statistics, Probability, Algebra, trigonometry, calculus, geometry, etc. All these specific subjects carry their concepts and rules. Similarly, factorial and factorization are two important terms in mathematics. How they are used? What is its significance? Do these terms are similar to each other? Along with them, we will cover major concepts in the following headings.
What is Factorial?
Before making big buildings, first strong the base! Clearing the concept will cover 50% of your work. Factorial is the property of a function that is represented by (!) and involves multiplying all whole numbers from our selected number to 1. Let’s simplify this statement.
For example:
We have selected the number 6. Its factorial will be:
6! = 6*5*4*3*2*1 = 720
We have multiplied our selected number i.e. (6) with all previous whole numbers to 1.
Factorial helps in simplifying the arrangement of a complicated number. And it increases the number of ways of arranging a series of numbers to 1. As shown by the resultant figure (720), it reveals that there are 720 different ways to arrange a series of numbers from 7 to 1.
Significance of Factorial:
In addition to showing the different ways of arrangements, factorial helps in determining the probability of a question. It will show how many times a number repeats or by how many ways a number can arrange?
This term is used in permutation and probability calculations.
How common Sense Helps in Understanding Factorial?
As we discussed that it reveals the number of ways to arrange a number. If we are destined to find the factorial of 2 we will focus that number “2” can only arrange in two ways to 1. i.e. (1, 2), (2, 1).
We can calculate factorial by this formula:
N! =n× (n−1)!
Where n shows the “number”
Factorial is the most common term in mathematics. If you are stuck at some point and could not figure out the exact answer try the factorial sequence calculator and have your result within a second.
Factorization:
Factorization, on the other hand, is the process to find the factors. Or it is the algebraic term in which a number may wrote as a product of the smaller numbers. It can be many factors in the same number. For example:
Factors of 12 can be:
12= 6*2
Or
12= 4*3
Or
12= 2*2*3
Factorization is one of the common terms in algebraic expressions in which the goal is to find a suitable number to multiply together and eventually get an expression as explained in the above example. Or it is splitting of a complex number into a multiplication of simple expressions. i.e. (splitting of 12 into 4*3) which is a simpler way.
Complexity in Factorization:
Factorization is easy to solve simpler expressions but its complexity rises as we got one level ahead. It is because we have to figure “what to multiply what” to have the desired expression. But practice can solve the problem.
Example:
Factor 42 – 9 can be solved by resolving the factor into simpler expressions like 2×2- 9 and 22– 32 so we have:
4x – 9 = (2)2 – (3)2
Conclusion:
You see that both terms factor and factorization are two vital and different terminologies used in algebraic expressions. Where one will use to find the factorial of numbers. The other will use to simplify complex expressions into simpler ones by finding suitable factors. These two concepts are easy but sometimes become difficult to comprehend. In such situations, you can release stress by using technology or online calculators. Which are easily available such as a Factoring calculator with steps which can be very handy. It will help you to solve the complex questions in split second.