Carcass wrote:
Let n = 11!. What is the smallest non-prime positive integer that is
not a factor of n?
enter your value GIVEN: x = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)We can clearly see that x is divisible by 11, 10, 9, . . . 3, 2 and 1
So, let's start checking integers that are greater than 11
Is 12 a factor of x?
x = (11)(10)(9)(8)(7)(
6)(5)(4)(3)(
2)(1)
= (11)(10)(9)(8)(7)(
12)(5)(4)(3)(1)
12 is clearly a factor of x
13 is prime, so we can skip that.
Is 14 a factor of x?
x = (11)(10)(9)(8)(
7)(6)(5)(4)(3)(
2)(1)
= (11)(10)(9)(8)(
14)(6)(5)(4)(3)(1)
14 is clearly a factor of x
At this point, we can see the pattern.
15 = (5)(3). Since 5 and 3 are both in the product 11!, we know that 15 is a factor of x
16 = (8)(2). Since 8 and 2 are both in the product 11!, we know that 16 is a factor of x
17 is prime - skip
18 = (6)(3)
19 is prime - skip
20 = (4)(5)
21 = (7)(3)
22 = (11)(2)
23 is prime - skip
24 = (3)(8)
25. (5)(5)
[aside: one 5 is hiding in the number 10]26 = (2)(13) HOLD ON! There is no 13 hiding in the product 11!
So, 26 cannot be a factor of 11!
Answer: 26
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep