PS Form25 sec2-Q20

[liyun]

請教

What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?

A 30
B 40
C 50
D 60
E 70

Ans:C

[chour]

求小於100的正整數,和100沒有相同因數的
100=2^2 * 5^2
小於100的正整數中:
2的因數50個,5的因數20個,10的因數10個
和100沒有相同因數的=100-(50+20-10)=40

我覺得答案是B,大家再討論看看囉~