[求助]再问一道prep的题 太难想了

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of aⁿ, what is the value of a ?

(1)  aⁿ = 64
                

(2)  n = 6

答案是B 我无法理解题目想表达什么 拜托NN帮忙解答一下吧

1*2*3*...*8 =(2^7)*(3^2)*(5)*(7), 如果这个是aⁿ 的倍数,(a 是 integer, n>1), 那么a只能含2或者3质因子，n可以是2，3。。。7

a=2,n=2,3,4,5,6,7

a=3,n=2

a=4,n=2,3

a=6,n=2

a=8,n=2

条件1不够，a can be 2 or 4;条件2充分，a=2