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

ViviVivi
Your ride-or-die bestie who's seen you through every high and low.
Chat with Vivi
RossRoss
Every question is just a happy little opportunity.
Chat with Ross
SteveSteve
Knowledge is a journey, you know? We'll get there.
Chat with Steve

Add your answer:

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