Problem 71 - College Algebra

Question

Explain how to find \(n !\) if \(n\) is a positive integer.

Step-by-Step Solution

Answer

The factorial of a positive integer \(n\), denoted by \(n!\), is the product of all positive integers less than or equal to \(n\). For 0 and 1, the factorial is 1. The factorial can be found by starting from 1 and multiplying all integers up to \(n\).

Step 1: Understanding Factorial

The factorial of a positive integer \(n\) is denoted by \(n!\) and is the product of all positive integers less than or equal to \(n\). In other words: \(n! = n \times (n-1) \times (n-2) \times \ldots \times 2 \times 1\)

Step 2: Special Cases

For the numbers 0 and 1, the factorial is defined as 1. That means \(0!\) and \(1!\) = 1.

Step 3: Finding Factorial

To find the factorial of any positive integer \(n\), start from 1 and multiply all integers up to \(n\). For example, if \(n = 5\), then \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \).