Question:
The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is
The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is
Show Hint
Use inclusion-exclusion on multiples of 2, 3 and 5 up to 100.
Updated On: Nov 5, 2026
- 26
- 18
- 31
- None
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Count the multiples:
Multiples of 2: 50; of 3: 33; of 5: 20. Of 6: 16; of 10: 10; of 15: 6. Of 30: 3.
Step 2: Inclusion-exclusion:
Divisible by at least one of 2, 3, 5: \(50 + 33 + 20 - 16 - 10 - 6 + 3 = 74\).
Step 3: Answer:
Not divisible by any: \(100 - 74 = 26\).
Final Answer:
The correct option is (1): 26.
Multiples of 2: 50; of 3: 33; of 5: 20. Of 6: 16; of 10: 10; of 15: 6. Of 30: 3.
Step 2: Inclusion-exclusion:
Divisible by at least one of 2, 3, 5: \(50 + 33 + 20 - 16 - 10 - 6 + 3 = 74\).
Step 3: Answer:
Not divisible by any: \(100 - 74 = 26\).
Final Answer:
The correct option is (1): 26.
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