超深數學, 好難

if n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

a. 10 or b. 11?
why?

The product of all the integers from 1 to n=A*990, A is +ve integer.
=A*2*5*9*11
As 11 is a largest prime number factor of this product, the least possible value n is 11 in order that the product is a multiple of 990.

2009-08-08 16:54:37 補充：
As 11 is the largest prime number factor of this product, the least possible value n is 11 in order that the product is a multiple of 990.

The product is: 1*2*3*4*5*6*7*8*9*10*11
=(1*2*3*4*5*6*7*8)(9*10*11)
=40320*990
=39916800

2009-08-08 16:55:53 補充：
The answer is b.11

2009-08-08 19:18:36 補充：
2009-08-08 17:12:16 補充問
what mean og multiple of 990?
乜唔係10咩?
10*99=990 喎?
答:
10 is not a multiple, it is only a multiplication factor of 990.
Multiples of 990 are 990, 1980, 2970, .....
Hope you understand now.