题目

What is the least positive integer that is not a factor of 25!and is not a prime
number?

提问时间：2020-07-13

答案

positive integers from smallest:
1,2,3,4,...
1 is a factor,25!=1*25!
2 is a prime number
3 is a prime number
4 is a factor,25!=4*1*2*3*5*6*...*25
25!指的是25阶乘=25*24*...*1
5显然是factor
6,7,8,9,10,...,25显然都是factor
26=2*13也是
27=3*3*3,25!中有3和9,所以也是factor
28=4*7,factor
29是prime
30=3*10
31prime
32=4*8,factor
33=3*11,factor
34=2*17,factor
35=5*7,factor
36=4*9,factor
37prime
38=2*19,factor
39prime
40=4*10,factor
41prime
42=2*21factor
43prime
44=4*11factor
45=5*9factor
46=2*23factor
47prime
48=6*8factor
49=7*7,25!包含7和14,factor
50=5*10factor
51=3*17factor
52=4*13factor
53prime
54=2*3*9,factor
55=5*11,factor
56=7*8,factor
57=3*19,factor
58=2*29,not a factor and not a prime
So 58 is the least positive integer that is not a factor of 25!and is not a prime number.