Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

Question

Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

1. A. 20
2. B. 21
3. C. 22 (Correct answer)
4. D. 23

Correct Answer

Option C — 22

Detailed Solution & Explanation

The correct answer is 22.

Key Points

• Using inclusion-exclusion for numbers 1–100 not divisible by 2, 3, 5, or 7 (9 is covered by 3).
• Count = 100 × (1−1/2)(1−1/3)(1−1/5)(1−1/7) = 100 × 1/2 × 2/3 × 4/5 × 6/7 ≈ 22.85. Exact count = 22. Answer: 22.