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## Comment on

Factorial Notation## Which of the following is a

a)2!+3

b) 4!+12

c)5!+6

d)5!+30

e)8!+12

How do i tackle this problem Brent? Do i have to consider prime numbers?

## Nice question!

Nice question!

If A and a multiple of B, then we can write A = kB for some integer k.

For example, we know that 24 is a multiple of 6, because we can write 24 = (4)(6)

4! + 6 = (4)(3)(2)(1) + 6

All MULTIPLES of 4! + 6 are in the form k(4! + 6), where k is an integers

k(4! + 6) = k[(4)(3)(2)(1) + 6]

= (k)(4)(3)(2)(1) + 6k

So, all multiples of 4! + 6 can be written in the form (k)(4)(3)(2)(1) + 6k

At this point, I SCAN the answer choices to see if any of them can be derived from the expression (k)(4)(3)(2)(1) + 6k

Notice that answer choice D, 5! + 30, can be derived if we let k = 5

That is, 5[4! + 6] = 5[(4)(3)(2)(1) + 6]

= (5)(4)(3)(2)(1) + 30

= 5! + 30

Answer: D

## Did you work backwards and

## Great question.

Great question.

I have edited my response above to address that question.

Cheers.

Brent

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