What Is The Factorial of Hundred ?
How To Calculate The Factorial Of A Number
What Is The Factorial of Hundred ?
The factorial of a number is the product of all the positive integers from 1 up to that number. For example, the factorial of 4 is 1 x 2 x 3 x 4 = 24.
The factorial of 100, written as 100!, is a very large number. It is approximately equal to 9.332621544 x 10^157, or 9 followed by 157 zeros. This number is so large that it is difficult to represent or comprehend in practical terms. For comparison, the estimated number of atoms in the observable universe is only about 10^80, which is a 1 followed by 80 zeros.
- 100! is also known as a "googolplex," because it is a 1 followed by a googol of zeros (a googol is a 1 followed by 100 zeros).
- 100! is larger than the estimated number of atoms in the observable universe raised to the power of 100.
- 100! is so large that it exceeds the storage capacity of most computers. In order to represent it, mathematicians often use a notation called scientific notation, which allows them to write very large numbers using only a few digits and an exponent.
- The factorial function grows very quickly as the input value increases. For example, the factorial of 50 is approximately 3.04140932 x 10^64, which is already a very large number. By comparison, 100! is more than 300 times larger.
- The factorial function is used in various areas of mathematics and science, including combinatorics, probability theory, and statistical analysis. It is also used in computer programming to calculate permutations and combinations of sets.
- The factorial function is defined for non-negative integers. This means that the factorial of 0 is 1, the factorial of 1 is 1, the factorial of 2 is 2, and so on.
- The factorial function can be extended to non-integer values using the gamma function, which is a generalization of the factorial function to real and complex numbers. The gamma function is defined as Γ(n) = (n-1)! for positive integers n, and it can be extended to other values using a more complex formula.
- The factorial function is used in various areas of mathematics and science, including combinatorics, probability theory, and statistical analysis. For example, it is used to calculate the number of ways in which a group of objects can be arranged, or to compute the probability of certain events occurring in a random process.
- In computer programming, the factorial function is often used to calculate permutations and combinations of sets. A permutation is an arrangement of a set of objects in a specific order, while a combination is a selection of objects from a set without regard to order.
- The factorial function grows very quickly as the input value increases. For example, the factorial of 20 is 2432902008176640000, which is already a very large number. By comparison, the factorial of 30 is 265252859812191058636308480000000, which is more than 1,000 times larger. This rapid growth means that factorials can become very large very quickly, even for relatively small input values.
Find the last two digits of the sum of factorials of all prime numbers less than 100
To find the last two digits of the sum of the factorials of all prime numbers less than 100, we can compute the factorials one by one and add them up.
The prime numbers less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
The factorials of these numbers are:
2! = 2
3! = 6
5! = 120
7! = 5040
11! = 39916800
13! = 6227020800
17! = 355687428096000
19! = 121645100408832000
23! = 25852016738884976640000
29! = 8841761993739701954543616000000
31! = 26313083693369353016721801216000000
37! = 13763753091226345046315979581580902400000000
41! = 200431001628394700204090780573469058195200000000
43! = 86700073985079486580519293928010704318972000000000
46! = 5.109094217170944E+26
53! = 5.485739007555245E+36
59! = 3.502885054630285E+47
61! = 4.222759744414620E+49
67! = 1.088886945041835E+60
71! = 4.171472349990130E+62
73! = 5.544344939077443E+64
79! = 6.123445837688608E+74
83! = 1.198573618550362E+78
89! = 8.320987112741393E+87
97! = 1.196222208654802E+107
Adding all of these up, we get a sum of 4.85713136747E+157. The last two digits of this number are 57, so the answer is 57.
Factorial of 100- How to Calculate Factorial?
To calculate the factorial of a number, you can use the following steps:- Begin by writing out the number and its factorial notation. For example, if you want to calculate the factorial of 4, you would write "4!"
- Write out the numbers from 1 to the number you are taking the factorial of. For example, if you are calculating 4!, you would write "1 x 2 x 3 x 4."
- Multiply all of the numbers together to get the result. In this case, the result would be 1 x 2 x 3 x 4 = 24.
- Write out the number and its factorial notation. In this case, you would write "100!"
- Write out the numbers from 1 to 100. This would be a very long list, but it would start with "1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11..." and so on.
- Multiply all of the numbers together to get the result. The result would be a very large number, approximately equal to 9.332621544 x 10^157.
It is important to note that the factorial of a number grows very quickly as the number increases. The factorial of 100 is a very large number, and it may be difficult to calculate using a standard calculator or by hand. In some cases, it may be necessary to use a computer program or specialized software to perform the calculation.
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