What is Factor and Factorial & How to Calculate them?
What is a Factor
Mathematically, the factors are described as numbers which equally or accurately divide the original number. The significance of the factor is any whole number that may equally divide any number greater than it.
In the case of prime number (the number that is only divisible by itself), it will have just two factors, i.e. 1 and number itself. On the other hand, any composite number, including s prime factors, will have more than two factors. It implies, finding two or more numbers values, the product of which being equal to the initial quantity is what known as factor.
For finding a common factor, first of all the most common monomial factor (factoring out common terms) of each term is identified, and then the original polynomial is divided by this, such that the second factor is obtained. The second factor in factorization however is always a polynomial.
How to Calculate Factor
The easiest approach to determine each and every factor of a number is to use the prime factorization method via the division method. To calculate factors by this method, you just have to start by dividing your numbers with the lowest integer, i.e. two and continue until it can’t be further divided by two.
As a next process then you have to begin with the number greater than the smallest one, i.e. 3. If in the first place the number is not divisible by 2, or is a prime number try dividing it up by 3, or 4, or by itself respectively.
Step by Step Factor Calculation
To calculate the factors of any number by prime factorization method is step by step described below. Considering the number 240 as an example:
- Divide by Smallest Number
First of considering the number whether it’s a prime number or not, start dividing it by the smallest possible integer. In our example, 240 is not a prime and an even number that means we can divide it by 2.
- Continue Division
After dividing it by 2 again divide it by the lowest possible number i.e. after 240/2 we get 120 which again can be divided by 2. For instance, in this step we would get 120/2 = 60. This division is continued until either he number isn’t divisible by two or we get 1 as the answer.
60/2 = 30
30/2 = 15
- Change Divisor
Now, you see that 15 can’t be divided by our smallest number, 2. So we have to change our divisor from 2 to the next possible divisor that would be three as per our example.
15/3 = 5
Again, the number 5 can’t be divided by 3, since we have to change our divisor. In this step, the next number also can’t divide 5, such that we have to jump to the next one from 4 i.e. 5.
5/5 = 1
As we have now got 1, the factoring process is completed. Also, if you do not want to follow these steps to calculate factor, you can try factor out calculator for online calculation.
What is a Factorial
In mathematics, the factorial is symbolized by the sign (!) or in wordy we would say it is denoted by an exclamation mark just after the symbol n. Whenever you come across number n! (also known as a ‘n factorial’) in statistical problems, it implies that a factorial is the product of all the whole numbers between 1 and n, whereas the n must always be a positive integer.
In mathematics therefore, a factorial is defined as a product of the numbers between n and 1. However, in order to prove that the product of no numbers equals one, we assert that 0! = 1. The factorial operation is found in a variety of fields of mathematics, including algebra, permutation and combination, and mathematical analysis, among others. The basic purpose of factorial is to enumerate ‘n’ potential different items.
Recursive Formula of Factorial
For factorial function, a recursive definition is also used in order to define it from another point of view. It defines the factorial function as, ‘n! = n*(n-1)!’ with the lowest recursion limit set to n = 2. While the factorial function performs repeated multiplication, its most evident mathematical purpose is to determine how many ways n items can be permutated.
The factorial simply instructs us to multiply any natural number by all of the natural numbers that are less than the number they are being multiplied with. For instance, if you are provided to determine 4!, all you have to do is multiply 4 by 3, by 2 times and then by 1.
By doing so you will get the answer 24. In the same manner, if the statement says to calculate 7! It implies 7 * 6 * 5 * 4 * 3 * 2 * 1 while giving 5,040 as a result. The same goes for any number value i.e. 30!. You have to follow this formula:
Here, 30! factorial implies 30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 that sequence. This factorial will give us the result 2.652528598 * 1032.
But sometimes there could be a larger number like 500!, 600! or maybe 3000!. In this case, one may spend about an hour on it. So we don’t need to spend our time on large calculations because the factorial expression calculator provides us that type of long calculations in a second with all the steps that we follow in our manual calculations.