2026-04-09

Problem — 2026-04-09

Easy

Easynumber_theory

How many positive integers from 11 to 100100 are not divisible by 22, 33, or 55?

Enter an integer

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By inclusion-exclusion: ∣div by 2∣=50|\text{div by } 2| = 50, ∣div by 3∣=33|\text{div by } 3| = 33, ∣div by 5∣=20|\text{div by } 5| = 20, ∣div by 6∣=16|\text{div by } 6| = 16, ∣div by 10∣=10|\text{div by } 10| = 10, ∣div by 15∣=6|\text{div by } 15| = 6, ∣div by 30∣=3|\text{div by } 30| = 3. So ∣div by 2, 3, or 5∣=50+33+20−16−10−6+3=74|\text{div by 2, 3, or 5}| = 50+33+20 - 16-10-6 + 3 = 74. Answer: 100−74=26100 - 74 = 26.