Skip to main content
Prime
← Back to archive

Problem #77 · October 12, 2026

Divisibility rules

Find the smallest natural number that is greater than 300300 and divisible by 22, 55 and 99.
  1. A310
  2. B315
  3. C330
  4. D360
  5. E450

WORKED EXAMPLE

Solution

For a number to be divisible by 22, 55 and 99, it must be divisible by EKUK(2;5;9)=90EKUK(2; 5; 9) = 90. The multiples of 9090: 270<300<360270 < 300 < 360. Therefore, the smallest number greater than 300300 is 360360.
Solve today's problem