LUANDATO wrote:What is the greatest value of x such that 3^x is a factor of 18!?
A. 9
B. 8
C. 6
D. 3
E. 2
The prompt implies the following:
18!/(3^x) = integer.
To determine the greatest possible value of x, we need to count how many 3's can divide into 18!.
Put another way:
We need to count how many 3's are contained within 18!.
The following multiples of 3 are contained with 18!:
3, 5, 9, 12, 15, 18.
If we factor out all of the 3's contained within the values above, we get:
3
6=
3*2
9=
3*
3
12=
3*4
15=
3*5
18=
3*
3*2.
The blue values indicate that there are eight 3's contained within 18!.
Implication:
Up to eight 3's can divide into 18!.
Thus, the greatest possible value of x = 8.
The correct answer is
B.
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