求助一道PREP数学题

gwendolyn6yeah

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. Between 2 and 10
B. Between 10 and 20
C. Between 20 and 30
D. Between 30 and 40
E. Greater than 40
谢谢~要过程哦~~

ryanzhang11

h（100）+1=2×4×6×……×100+1=2×（50!）+1  如果这个质因子小于50 则h（100）+1 会余1 因为等式去掉1的话包含了小于50的所有数 所以加上1就除不尽了 与“这个质因子小于50”的假设冲突了就 所以是大于50的

anitawin

LS童鞋好思路！我是把值算出来然后按选项挨个验证的 笨办法。。。

gwendolyn6yeah

谢谢2Lnn~~