Factorials!

What is a Factorial? A factorial is the result of multiplying a sequence of descending whole, positive numbers. For example, 4 x 3 x 2 x 1

How do we represent this? Because mathematicians like to have a symbol for everything, they came up with one for factorials! How can we write 4 x 3 x 2 x 1 4 x 3 x 2 x 1 = 4!

The Factorial Function Essentially, the symbol ! means to multiply all of the whole, positive numbers that are equal to or less than the value in front of ! Evaluate: 4! 6! 1!

We can use previously calculated factorials to find new ones Use the chart to fill in the missing values nn! 11!= 1 22!= 2 x 1= 2 x 1! 33! 44! 55! 66!

Example If 9! = 362, 880, find the value of 10!

What about 0! Zero Factorial is interesting Just like many other properties involving 0, including 2⁰ = 1, we can evaluate 0! It is generally agreed that 0! = 1

A List of Factorials nn! , , , ,628, ,916, ,001, ,227,020, ,178,291, ,307,674,368, ,922,789,888, ,687,428,096, ,402,373,705,728, ,645,100,408,832, ,432,902,008,176,640, ,090,942,171,709,440, ,124,000,727,777,607,680, ,852,016,738,884,976,640, ,448,401,733,239,439,360, ,511,210,043,330,985,984,000,000

Example Evaluate 7! 4!

Example Evaluate 8! 3!

Example Evaluate 11! 6!

Example Evaluate 9! 5!4!

Example Evaluate 12! 7!5!

Example Write 7! + 8! as the product of a whole number and a factorial number. (Do not calculate the factorials)

Example Write 60! + 61! as the product of a whole number and a factorial number. (Do not calculate the factorials)

Example Write 11! - 10! as the product of a whole number and a factorial number. (Do not calculate the factorials)

Example Write 19! - 17! as the product of a whole number and a factorial number. (Do not calculate the factorials)

Example