FACTORIAL OF A NUMBER

Calculation of the factorial of a number remains a significant part of quantitative aptitude. But, for developing an understanding regarding this, a preliminary idea of “integers” is important. In mathematics, “integer” refers to a “whole number” which means a number that is not represented as a fraction. For example- 2, 4, 7, etc. are integers whereas 9.75, 4.25, 1.80, etc. cannot be referred to as “integers” as these numbers are present in the form of fractions. Therefore, it can be stated that the factorial of a definite number is the multiplication product of all the “integers” or “whole numbers” having less value than the concerned number. 

Quantitative Aptitude

The word “quantitative” represents a measurement of something by its quantity. It is antagonistic to “qualitative” in which the measurement is done by the quality of something. In other words, “quantitative” includes numerical data that can be calculated. “Quantitative aptitude” represents the skill and ability of an individual in solving mathematical problems (toppr.com, 2022). This term is closely associated with the “aptitude tests”. This kind of test or examination is organized for judging the ability of the potential candidates to solve the given mathematical problems within a set deadline (careers360.com, 2022). At present, such tests play a key role in the selection of potential and skilled employees for an organization. The testing of “quantitative skill” is an integral part as it helps the organizations to understand how much ability an individual possesses while dealing with complex numerical data within a given period. In such “aptitude exams”, the skill regarding solving problems on “partnership”, “data interpretation”, “height and distance”, “number”, “calendar”, “pipe and cistern”, “boat and stream”, “simple and compound interest”, “profit and loss”, “mixture and alligation”, “percentage”, “speed, time and distance”, “clock”, etc. are checked. Apart from these, calculation regarding the “Factorial” of a number is also asked in such exams.

Factorial of a Number Using for Loop

For the calculation of factorials, only whole numbers or integers can be considered. But, a negative integer cannot be taken for the calculation of factorial. Therefore, a factorial can only be calculated only when the whole number is either a zero or positive. The calculation procedure of factorial is simple. The formula for calculation of factorial is (cuemath.com, 2022)-

n! = n * (n-1)!

Following the above-mentioned formula, the factorial of the integer 5 is 120. Following is the calculator procedure-

5! = 5*4*3*2*1 = 120

In this calculation, all the whole numbers having less value than 5 have been multiplied with the concerned integer 5 for producing the factorial value of this number. Factorial of a Number Use of Factorial in Mathematics

From the above discussion, it has been evident that the calculation process of factorial is quite simple. Wide use of factorial calculation is seen in the case of “permutation-combination”. This is another interest as well as an integral part of quantitative aptitude. This helps to understand multiple ways by which the sets of an object can be arranged. The mathematical formula for the calculation of permutation is –

nPr = n!/(n−r)!

 The mathematical formula for calculating combination is as follows-

nCr = n!r!(n−r)!

Therefore, it is evident that without the calculation of factorial, the answers of permutation, as well as the combination, cannot be produced.

Conclusion 

The factorial calculation is an important part of quantitative aptitude as knowledge regarding factorial lays the foundation for solving problems related to probability and calculus. The calculation procedure of factorial is a simple technique that involves only multiplication. When the integers having a lower value than the number for which factorial is being calculated gets multiplied with the number itself, reproduces the factorial value. Apart from the probability problems, the factorial calculation acts as a major part of permutation-combination-related mathematical problems too.