Skip to main content
Prime
← Back to archive

Problem #74 · October 9, 2026

Divisibility rules

How many natural numbers from 100100 to 400400 are multiples of 77?
  1. A42
  2. B43
  3. C44
  4. D45
  5. E57

WORKED EXAMPLE

Solution

The smallest multiple of 77 in the interval is 7⋅15=1057 \cdot 15 = 105, and the largest is 7⋅57=3997 \cdot 57 = 399. There are 57−15+1=4357 - 15 + 1 = 43 of them. When finding the number of terms, it is important not to forget +1+1.
Solve today's problem