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+2016106+3=74|\text{div by 2, 3, or 5}| = 50+33+20 - 16-10-6 + 3 = 74. Answer: 10074=26100 - 74 = 26.