curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?
A. 2
B. 4
C. 6
D. 8
E. 10
Let’s put the even numbers from 2 to 10 in prime factors.
2
4 = 2^2
6 = 2 x 3
8 = 2^3
10 = 2 x 5
We see that there are 8 prime factors of 2 in 10!, so 8 is the value of n.
Alternate Solution:
We know that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Let’s find all the 2’s in this product.
The number 10 contributes 1 two.
The number 8 contributes 3 twos.
The number 6 contributes 1 two.
The number 4 contributes 2 twos.
The number 2 contributes 1 two.
Thus, we have a total of 8 twos, and so 8 is the value of n..
Answer: D
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