Exploring the Divisibility and Factorial of the Number 8
Understanding the properties of numbers, such as the number 8, involves exploring both its divisibility and its factorial. This article will delve into the factors of 8 and calculate the factorial of 8, providing a comprehensive overview for those interested in learning more about these mathematical concepts.
Factors of 8
A factor of a number is any integer (whole number) that can be multiplied by another integer to produce that number. For the number 8, its factors are the integers that can divide 8 without leaving a remainder. Letrsquo;s break it down step by step:
Prime Factorization
First, we start by performing the prime factorization of 8:
8 can be expressed as 2 x 4. Continuing the factorization, 4 can be expressed as 2 x 2. Therefore, the prime factorization of 8 is 2 x 2 x 2, or 23.The Factors
From the prime factorization, we can identify all factors of 8 by combining these prime factors in different ways:
1 (because 1 x 8 8) 2 (because 2 x 4 8) 4 (because 2 x 2 x 2 8) 8 (because 2 x 2 x 2 8)Factorial of 8
The factorial of a number is the product of all positive integers less than or equal to that number. The factorial of 8 is written as 8! and is calculated as follows:
Calculation of 8!
We write out the numbers from 1 to 8: 1, 2, 3, 4, 5, 6, 7, 8. Next, we multiply these numbers together: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Performing the multiplication step-by-step: 8 x 7 56 56 x 6 336 336 x 5 1680 1680 x 4 6720 6720 x 3 20160 20160 x 2 40320 40320 x 1 40320Therefore, the value of 8! is 40320. This can also be verified using a calculator or a mathematical software.
Conclusion
By exploring the factors and factorial of the number 8, we have gained insight into important mathematical concepts. Factors of 8 include 1, 2, 4, and 8, while the factorial of 8 (8!) is 40320. Understanding these concepts not only enhances mathematical skills but also lays a strong foundation for more advanced studies in mathematics.