求翻译...求详解.apositiveintegerissaidtobe"tri-factorable"ifitistheproductofthreeconsecutiveintegers.howmanypositiveslessthan1000aretri-factorable?

Question

求翻译...求详解.
a positive integer is said to be "tri-factorable" if it is the product of three consecutive integers. how many positives less than 1000 are tri-factorable?

Answer 1

1000以内,有多少个数是三个连续整数的乘积.
这样考虑,1000=10*10*10,因此这三个连续整数必然不能都大于10.
1,2,3
2,3,4
3,4,5
...
可以想到,最大的那组数是9,10,11.
因此1000以内,共有9个thr-factorable