Just count all the factors of 3 in 30!.kumar720 wrote:If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18
OA[spoiler]:C[/spoiler]
Help me solving the problem
3 x 3 x 3^2 x 3 x 3 x 3^2 x 3 x 3 x 3^3 x 3 = 3^14. Each multiple of 3 in the product will add one additional factor of 3, each multiple of 9 will add one more on top of that, and each multiple of 27 will add one more on top of that.
From left to right, the 3s come from the following integers in the product: 3,6,9,12,15,18,21,24,27,30. You can see 9 and 18 have a total of 2 factors of 3, and 27 has 3.
No need to memorize any sort of formula to answer this... It should take no more than a minute to count the factors of 3.
