Factorial Calculator(n!) - Best free Online Factorial Calculator. Easiest Way to get the Factorial of the number.
| Result: |
What is Factorial ?
In mathematical concept, the end product of given postive(+) integers(n) or number is called as factorial of that number which is denoted by "n!". Factorial is also called as the end product of an integer and all the integers falling under it. For example : The factorial of Number 3 (3!) is equals to 6 (3 x 2 x 1= 6). Factorial calculations are occured in many areas of maths just like in case of mathematical analysis, algebra, combinatorics etc. Earlier in 12th century 'Indian Scholars' started using the trend of factorial calculations for counting permutations. In 1808 one of the well-known french mathematician Christian Kramp introduced the notation of 'n!' for factorial. The basic formula for defining the factorial function is : n! = 1.2.3...(n-2).(n-1).n i.e for example 5! = 5 x 4 x 3 x 2 x 1 = 120.
How to use Factorial Calculator ?
It is very simple to use this factorial calculator. You just have to enter the number in the factorial calculator in the first box and just press the 'calculate' button. Your result i.e the factorial of given number will be displayed in the second box.
Basic Factorial Calculation Problems
Factorial Problem no 1
Q. A deck of playing cards has 13 hearts. There are how many ways with which these 13 hearts can be arranged ?
Solution :
The solution of this factorial problem is very easy. It involves calculating the factorial. As we want to know how these 13 cards of heart can be arranged, we need to calculate the value of 13 factorial ( 13! ).
13!= 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 6,227,020,800
Note : These calculations can be time consuming by solving with just pen and paper. So you can just head upto above factorial calculator and just get your answer within blinking your eye.
Factorial Problem no 2
Q. There are how many different ways with which the letters in the word 'background' can be arranged ?
Solution :
For solving this problem, we just have to take the number of letters in the given word and find the factorial of that number. In these problem all the letters in the given word are unique and non-repeated. Therefore total number of letters in the given word are 10, so we have to find the factorial of number 10.
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3.6288 E+6.
Factorial Problem no 3
Q. 8! x 5!
Solution :
Now in this problem to get the solution, we have to multiply the factorial of 8 with the factorial of 5.
Factorial of 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
Factorial of 5! = 5 x 4 x 3 x 2 x 1 = 120
40320 x 120 = 4838400
Factorial Problem no 4
Q. 7! / 6!
Solution :
Now in this problem to get the solution, we have to divide the factorial of 7 with the factorial of 6.
Factorial of 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
Factorial of 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
5040 / 720 = 7
Factorial Problem no 5
There are how many different way that 8 people can come 1st, 2nd and 3rd?
Solution :
Now first let us name the numbers in alphabetically order. Let us assume that 8 people are called a, b, c, d, e, f, g, h then the list will go quite long.
abc, abd, abe, abf, abg, abh, acb, acd, ace, acf, ... etc.
The formula to solve this Factrorial Problem is 8!/(8-3)! = 8!/4!
Note: By using above factorial calculator you can easily get the factorials of 8 and 4
Now by writing the multiplies in full we get,
( 8 x 7 × 6 × 5 × 4 × 3 × 2 × 1 / 4 × 3 × 2 × 1 ) = 8 x 7 x 6 x 5 (remaining numbers get cancelled out each other)
= 8 x 7 x 6 x 5 = 1680
So there are almost 1680 ways that 8 people can come 1st, 2nd and 3rd.
Factorial Problem no 6
In how many ways can 4 cricket players and 4 football players be selected from 11 cricket players and 15 basketball players team ?
Note :
Generally, Factorial is one of the mathematical way used to determine or measure the product of a number with its lower value. For example, the factorial of three is 3! = 3 × 2 × 1. Factorial is most commonly used to determine the permutation or combination in statistics. And one can really need a factorial calculator in handy to solve this tricky problems.
Solution :
Given -
The total number of selected cricket player is n1 = 4
The total number of selected basketball player is n2 = 4
The total number of cricket players n3 = 11
The total number of basketball players n4 = 15
By using this relation, the number of ways is calculated as follows :
11! x 15!
(11 - 4)! (4!) (15 - 4)! (4!)
11! x 15!
(7)! (4!) (11)! (4!)
11 x 10 x 9 x 8 x (7!) x 15 x 14 x 13 x 12 x (11!)
(7!) (4!) (11!) (4!)
11 x 10 x 9 x 8 x 15 x 14 x 13 x 12
(4!) (4!)
7920 x 32760
24 24
Ans = 450450
Factorial Problem no 7
Evaluate 14! 8!
12! 6!
Solution :
Generally for this type of problems, evaluating each factorial is not necessary. But for better understanding we have done it for you.
All thanks to the above factorial calculator due to which finding factorial of any number is on the go.
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479001600
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
14! = 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 87178291200
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
It can be solved by 2 methods :
Method 1 :
14!8!
12!6!
(14 x 13 x 12 x 11x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
(12 x 11x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) (6 x 5 x 4 x 3 x 2 x 1)
(87178291200)(40320)
(479001600)(720)
Ans = 10192
Method 2 :
14! 8!
12! 6!
(14 x 13 x 12 x 11x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)(8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
(12 x 11x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)(6 x 5 x 4 x 3 x 2 x 1)
As you can see the common factors in numerator and denominator gets cancelled on both L.H.S and R.H.S
(14 x 13) (8 x 7)
182 x 56
Answer = 10192
How to Find Factorials Using Factorial Calculator Ti 84 Plus ?
Below Video Explains You the step by step procedure to find the factorials by using a factorial calculator Ti 84 Plus.
| Number | Factorial |
| 1! | 1 |
| 2! | 2 |
| 3! | 6 |
| 4! | 24 |
| 5! | 120 |
| 6! | 720 |
| 7! | 5040 |
| 8! | 40320 |
| 9! | 362880 |
| 10! | 3628800 |
| 11! | 39916800 |
| 12! | 4790016000 |
| 13! | 6227020800 |
| 14! | 8717821200 |
| 15! | 1307674368000 |