answersLogoWhite

0

9! = 9×8×7×6×5×4×3×2

Separate each of the above factors into prime and non-prime:

Prime

2

3

5

7

Non-prime

4

6

8

9

Perform a prime factorization of each of the non-prime factors:

4 = 22

6 = 3×2

8 = 23

9 = 32

Rewrite the number using these prime factorizations:

9! = 32 × 23 × 7 × (3×2) × 5 × 22 × 3 × 2

Group:

9! = 7 × 5 × 34 × 27

For any number with factors (greater than 1) of aA × bB × cC × ... × nN , it can be shown that the total number of divisors is (A+1)×(B+1)×(C+1)× ... × (N+1). This is because there are N+1 possible ways to divide out the factor n to create a unique divisor (n0 is also a factor). Using basic combinatorics, the total possible number of divisors is simply the products of all these possibilities for each prime factor.

Therefore, the number of divisors in 9! can be computed as follows:

(1+1)(1+1)(4+1)(7+1) = 160

Thus, 9 factorial has 160 divisors.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
ProfessorProfessor
I will give you the most educated answer.
Chat with Professor
BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake

Add your answer:

Earn +20 pts
Q: How many divisors does 9 factorial have?
Write your answer...
Submit
Still have questions?
magnify glass
imp