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 – Creator of greenlighttestprep.com

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