Simple factorial problem

Question

How do I solve the following?

$$\dfrac{76!}{76!-75!}$$

$76! - 75! = 76(75!)-75! = 75!(76-1) = 75(75!)$ and so you have $$\frac{76(75!)}{75(75!)}$$ — Matthew Cassell, Dec 01 '16 at 01:29
Possible duplicate of Highest power of a prime $p$ dividing $N!$ — Shailesh, Feb 21 '17 at 01:40

score 3 · Accepted Answer · answered Dec 01 '16 at 01:30

3

$$76! = 76\cdot 75!$$

$$\frac{76!}{76!-75!} = \frac{75!\cdot 76}{75!(76-1)} = \frac{76}{75} $$

answered Dec 01 '16 at 01:30

Mark Fischler

score 2 · Answer 2 · answered Dec 01 '16 at 01:29

2

HINT

76! = 76*75! Plug that in and see what you get

answered Dec 01 '16 at 01:29

Bram28

score 1 · Answer 3 · answered Dec 01 '16 at 01:31

1

Note that $76!=76*75!$ and that $76!-75!=75!(76-1)$, so then we see that $\frac{76!}{76!-75!}=\frac{76*75!}{75!(76-1)}=\frac{76}{75}$

answered Dec 01 '16 at 01:31

AndroidFish

3 Answers3