How many integers in the set {1, 2, 3, …, 100} have exactly 3 divisors?
समुच्चय {1, 2, 3, ..., 100} में ऐसे कितने पूर्णांक हैं जिनके ठीक 3 भाजक हैं?
This Question Asked In:
SSC, CGL
Correct Answer :B - 4
Detailed Text Solution
A number has exactly 3 divisors if and only if it is the square of a prime number.
So we need prime numbers whose squares are less than or equal to 100.
Prime numbers ≤ √100 = 10 are:
2, 3, 5, 7
Their squares are:
2² = 4
3² = 9
5² = 25
7² = 49
All are within 100.
Thus, there are 4 such integers.