1. Factorials!

2. 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

3. 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!

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!

5. 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!

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

7. 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

8. A List of Factorials nn! 01 11 22 36 424 5120 6720 75,040 840,320 9362,880 103,628,800 1139,916,800 12479,001,600 136,227,020,800 1487,178,291,200 151,307,674,368,000 1620,922,789,888,000 17355,687,428,096,000 186,402,373,705,728,000 19121,645,100,408,832,000 202,432,902,008,176,640,000 2151,090,942,171,709,440,000 221,124,000,727,777,607,680,000 2325,852,016,738,884,976,640,000 24620,448,401,733,239,439,360,000 2515,511,210,043,330,985,984,000,000

9. Example Evaluate 7! 4!

10. Example Evaluate 8! 3!

11. Example Evaluate 11! 6!

12. Example Evaluate 9! 5!4!

13. Example Evaluate 12! 7!5!

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

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

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

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

18. Example