我知道是gwd但是找不到在哪里了?表好意思了.

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10

B. 12

C. 14

D. 16

E. 18

我觉得这个k,怎么会是算1-30里面有多少个3呢?实在头疼死了.麻烦帮助点解一下阿.

p=1×2×3×4~~~~~~~~×30

p的最大因子3^k ＝3×6×9×12×15×18×21×24×27×30＝N×3¹⁴

^{N为其余的因子}

^{so，k的最大值为14}