AchyuthReddy wrote:

What is the smallest positive integer that is non-prime and not a factor of 9!?

-----ASIDE---------------------

A lot of integer property questions can be solved using prime factorization.

For questions involving divisibility, divisors, factors and multiples, we can say:

If N is divisible by k, then k is "hiding" within the prime factorization of NConsider these examples:

24 is divisible by

3 because 24 = (2)(2)(2)

(3)Likewise, 70 is divisible by

5 because 70 = (2)

(5)(7)

And 112 is divisible by

8 because 112 = (2)

(2)(2)(2)(7)

And 630 is divisible by

15 because 630 = (2)(3)

(3)(5)(7)

-----ONTO THE QUESTION!---------------------

9! = (9)(8)(7)(6)(5)(4)(3)(2)(1)

So, 1 to 9 are definitely factors of 9!

10 is also a factor of 9! since 9! = (9)(8)(7)(6)(

5)(4)(3)(

2)(1) = (9)(8)(7)(6)(

10)(4)(3)(1)

11 is prime, so we can ignore that.

12 is also a factor of 9! since 9! = (9)(8)(7)(

6)(5)(4)(3)(

2)(1) = (9)(8)(7)(6)(

12)(4)(3)(1)

Using the same logic, we can show that 14, 15, 16, 18, 20 and 21 are all factors of 9!

However, 22 is NOT a factor of 9!

We know this because 22 = (2)(11) and there is no 11 hiding in the prime factorization of 9!

Answer: 22

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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