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

n n!1 1! = 1 = 1

2 2! = 2 x 1 = 2 x 1!

3 3!

4 4!

5 5!

6 6!

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 Factorialsn n!0 11 12 23 64 245 1206 7207 5,0408 40,3209 362,880

10 3,628,80011 39,916,80012 479,001,60013 6,227,020,80014 87,178,291,20015 1,307,674,368,00016 20,922,789,888,00017 355,687,428,096,00018 6,402,373,705,728,00019 121,645,100,408,832,00020 2,432,902,008,176,640,00021 51,090,942,171,709,440,00022 1,124,000,727,777,607,680,00023 25,852,016,738,884,976,640,00024 620,448,401,733,239,439,360,00025 15,511,210,043,330,985,984,000,000

Example

Evaluate7!4!

Example

Evaluate8!3!

Example

Evaluate11! 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