What is 17 factorial ?

In mathematics, a factorial is a function that multiplies a given number by every natural number less than itself, down to 1. This function is especially interesting when we look at 17!, or the factorial of 17, because it represents a large number that has significance in various mathematical frameworks and applications. Understanding the factorial of 17 helps to grasp the enormous quantities and permutations that factorials can represent.

The basic formula to calculate the factorial of a number is n! = n × (n-1) × … × 1. To calculate 17!, you start with the number 17 and multiply it by every positive whole number less than it until you reach 1. It looks something like this:
17! = 17 × 16 × 15 × … × 3 × 2 × 1.
The exact calculation extends into a very large number, which exemplifies the exponential growth of factorials with larger initial numbers.

The factorial function has several practical applications, particularly in the realms of combinatorics and probability theory. When calculating the number of different ways to arrange or combine a certain number of objects, factorials are of paramount importance. Specifically, 17! can be significant when dealing with problems involving the arrangement of 17 distinct objects or scenarios where combinations need to be calculated in large sets.

• 1. Without calculating the full value, determine whether 17! is an even or odd number.
• 2. Estimate the number of zeros at the end of the number 17!.
• 3. Imagine you have a deck of 17 unique cards. How many different ways can you arrange these cards in order?

1. 17! includes the number 2, which means it is an even number.
2. The number of zeros at the end of 17! can be estimated by calculating the number of times 10 can be factored out; since 10 is 2 times 5, and there are more twos than fives, we need to count the number of fives, which is 3, resulting in 3 zeros.
3. There are exactly 17! ways to arrange a deck of 17 unique cards, which is an exceedingly large number.