In mathematics, many magical numbers have some unique properties. Due to these properties, these numbers become very rare, such as the concept of prime numbers, which tells about the numbers that can only be divided by one or themselves. However, prime numbers are not very rare. There are numbers and series that are much rarer than prime numbers.
Strong numbers are one of the rarest numbers in mathematics that possess some properties that can't be found in every number. In this blog, you will learn about the concept of strong numbers. Moreover, you will also learn about some programs related to such numbers.
What is a Strong Number in Mathematics?
The concept of strong numbers is about the sum of the factorials of the digits of a number. If the sum of the factorials of the number digits turns out to be equal to the number itself, the number is said to be a strong number. Moreover, in order to be a strong number, the number should also be a positive integer.
Here is an example to simply learn about the concept of strong numbers.
145 is one of these numbers in mathematics. Let's see how?
First, find out the factorial of each digit of the number 145.
1! = 1
4! = 4×3×2×1 = 24
5! = 5×4×3×2×1 = 120
Now, sum up all the factorials of all digits of 145.
145 = 1! + 4! + 5!
145 = 1+ 24 + 120
145 = 145
As you can see, the factorial sum of all the digits 145 is equal to 145 itself. Therefore, it is a strong number.
Significance of Strong Numbers in Mathematics
The history and significance of strong numbers can be traced back to the field of number theory. This theory has been a subject of mathematical exploration for centuries. However, the concept of a strong number is not very historic.
The specific term “strong number” gained prominence in the modern era of mathematics. But the concept of factorial is comparatively older. The study of factorials dates back to ancient civilizations. The factorial concept is essential for such numbers and can also be called the backbone.
Finding Strong Numbers with Programming
Now, let's learn about writing programs related to strong numbers. There are two very popular and essential programs that you can use in your programming projects.
- Python program to find if a number is a strong number or not
The above program functions to find if a number is a strong number or not. Here's an overview of how this program works.
The Python program has a function called ‘factorial().' This function in the program is responsible for finding out the factorial of the input. Moreover, there is another function, “is_strong_number(),” which uses the first function and finds out if the number that is taken as input is a strong number or not.
It sums up the factorial of all the input digits, and if the result turns out to be equal to the input, it prints “input is a strong number;” otherwise, it prints “input is not a strong number.”
After running the above code in an online Python compiler, it will ask you to “Enter a number.”
Now, upon entering a positive integer and pressing “Enter,” the compiler will print the number with either an “is a strong number” statement or a “is not a strong number” statement. Here, the number is 2, which is a strong number, so the program printed “2 is a strong number.”
- Python program to find the strong numbers between two numbers
In the above image, the Python program finds all the strong numbers that exist between any two given numbers. It also has the same two functions, “factorial()” and “is_a_strong_number(),” to identify if the number is strong or not by the same method.
However, here the program asks for starting and ending numbers, creating a series of numbers from which these numbers must be found.
The third function, “generate_strong_number,” is responsible for going through the given range of numbers and checking every single number with the above two functions.
If the result comes true, it means the number is a strong number, and it prints the number and moves on to the next number. If the result comes as false, it means the number is not a strong number, and it skips printing the number.
The program ends when it reaches the last number of the given range, and as a result, it declares the numbers that are strong numbers between the given range.
When you run the code, it will ask you “enter the starting number:”
Enter any positive integer such as “1” and press enter. The program will ask you, “Enter the ending number:”
Here, you should put any number greater than the starting number so that all the numbers in the range will be positive integers. Being a positive integer is one of the conditions for being a strong number.
If you try to put a negative integer or a smaller number than the starting number, it will not print the correct answer.
Here the ending number is 1000, and the program has printed [1, 2, 145] as the result.
Similarly, you can find a strong number using programs written in other languages. Python and C programs for finding them are more simple compared to other languages. However, the working of these programs in almost every language remains the same.
Relation Between Strong Numbers and computer organization and architecture
Strong numbers and computer organization and architecture may seem unrelated at first glance, but there is a fascinating connection between the two.
Strong numbers, which are positive integers that equal the sum of their factorials, to exhibit a unique pattern when analyzed from a computational perspective.
Calculating factorials involves repetitive multiplication, which can be efficiently implemented using algorithms such as the iterative or recursive approach. This process mirrors the fundamental building blocks of computer architecture, where multiplication operations are crucial for various computations.
Exploring the properties and computations of strong numbers provides insights into the underlying mechanisms and optimizations of computer organization and architecture.
Conclusion
The concept of a strong number is one of the magical concepts of mathematics found by humans. It is an excellent concept of rare numbers that have very unique properties.
Moreover, you should try to learn about many unsolved mysteries related to these numbers at least once. The algorithms associated with this concept are also great to learn about.
