What is 30 factorial ?

A factorial, denoted by an exclamation mark (!), is a mathematical function that multiplies a number by every natural number below it down to 1. Understanding the factorial of 30 (30!) is significant in mathematics as it represents a count of possible permutations for 30 distinct items, which arises in various complex calculations within the realms of probability, combinations, and more.

The factorial of a number n is calculated with the formula n! = n × (n-1) × … × 1. When this is applied to the number 30:

30! = 30 × 29 × 28 × … × 2 × 1

Due to the immense size of this calculation, it is commonly computed with calculators or computer programs.

The factorial of a number finds its application in several diverse fields. The factorial of 30 (30!) is especially prevalent in combinatorics and probability theory, where it’s used to determine the number of ways to arrange or combine items from a set of 30 elements. It also surfaces in mathematics problems involving series and mathematical analysis.

• Without calculating the exact number, estimate whether the factorial of 30 is greater or smaller than 10^30 and explain why.
• How many zeros are there at the end of the value of 30 factorial?

1. The factorial of 30 is greater than 10^30. This is because the factorial represents the product of all numbers from 1 to 30, many of which are greater than 10, thus making the product substantially larger than 10 raised to the 30th power.

2. There are 7 zeros at the end of the value of 30 factorial. This can be deduced by counting the number of multiples of 5 in the range 1 to 30 (there are 6), and since there is an adequate number of twos to pair with fives to make tens, we simply count the number of fives.